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Your data matches 4 different statistics following compositions of up to 3 maps.
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Matching statistic: St000410
St000410: Ordered trees ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[]]
=> 2
[[],[]]
=> 3
[[[]]]
=> 6
[[],[],[]]
=> 4
[[],[[]]]
=> 8
[[[]],[]]
=> 8
[[[],[]]]
=> 12
[[[[]]]]
=> 24
[[],[],[],[]]
=> 5
[[],[],[[]]]
=> 10
[[],[[]],[]]
=> 10
[[],[[],[]]]
=> 15
[[],[[[]]]]
=> 30
[[[]],[],[]]
=> 10
[[[]],[[]]]
=> 20
[[[],[]],[]]
=> 15
[[[[]]],[]]
=> 30
[[[],[],[]]]
=> 20
[[[],[[]]]]
=> 40
[[[[]],[]]]
=> 40
[[[[],[]]]]
=> 60
[[[[[]]]]]
=> 120
[[],[],[],[],[]]
=> 6
[[],[],[],[[]]]
=> 12
[[],[],[[]],[]]
=> 12
[[],[],[[],[]]]
=> 18
[[],[],[[[]]]]
=> 36
[[],[[]],[],[]]
=> 12
[[],[[]],[[]]]
=> 24
[[],[[],[]],[]]
=> 18
[[],[[[]]],[]]
=> 36
[[],[[],[],[]]]
=> 24
[[],[[],[[]]]]
=> 48
[[],[[[]],[]]]
=> 48
[[],[[[],[]]]]
=> 72
[[],[[[[]]]]]
=> 144
[[[]],[],[],[]]
=> 12
[[[]],[],[[]]]
=> 24
[[[]],[[]],[]]
=> 24
[[[]],[[],[]]]
=> 36
[[[]],[[[]]]]
=> 72
[[[],[]],[],[]]
=> 18
[[[[]]],[],[]]
=> 36
[[[],[]],[[]]]
=> 36
[[[[]]],[[]]]
=> 72
[[[],[],[]],[]]
=> 24
[[[],[[]]],[]]
=> 48
[[[[]],[]],[]]
=> 48
[[[[],[]]],[]]
=> 72
[[[[[]]]],[]]
=> 144
Description
The tree factorial of an ordered tree.
Matching statistic: St001813
Values
[[]]
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 2
[[],[]]
=> ([(0,2),(1,2)],3)
=> ([(0,1),(0,2)],3)
=> 3
[[[]]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 6
[[],[],[]]
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3)],4)
=> 4
[[],[[]]]
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,2),(0,3),(3,1)],4)
=> 8
[[[]],[]]
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,2),(0,3),(3,1)],4)
=> 8
[[[],[]]]
=> ([(0,3),(1,3),(3,2)],4)
=> ([(0,3),(3,1),(3,2)],4)
=> 12
[[[[]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 24
[[],[],[],[]]
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4)],5)
=> 5
[[],[],[[]]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(4,1)],5)
=> 10
[[],[[]],[]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(4,1)],5)
=> 10
[[],[[],[]]]
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ([(0,3),(0,4),(4,1),(4,2)],5)
=> 15
[[],[[[]]]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> 30
[[[]],[],[]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(4,1)],5)
=> 10
[[[]],[[]]]
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(3,2),(4,1)],5)
=> 20
[[[],[]],[]]
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ([(0,3),(0,4),(4,1),(4,2)],5)
=> 15
[[[[]]],[]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> 30
[[[],[],[]]]
=> ([(0,4),(1,4),(2,4),(4,3)],5)
=> ([(0,4),(4,1),(4,2),(4,3)],5)
=> 20
[[[],[[]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,4),(3,2),(4,1),(4,3)],5)
=> 40
[[[[]],[]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,4),(3,2),(4,1),(4,3)],5)
=> 40
[[[[],[]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ([(0,3),(3,4),(4,1),(4,2)],5)
=> 60
[[[[[]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 120
[[],[],[],[],[]]
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> 6
[[],[],[],[[]]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> 12
[[],[],[[]],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> 12
[[],[],[[],[]]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> 18
[[],[],[[[]]]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
=> 36
[[],[[]],[],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> 12
[[],[[]],[[]]]
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> 24
[[],[[],[]],[]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> 18
[[],[[[]]],[]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
=> 36
[[],[[],[],[]]]
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> ([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> 24
[[],[[],[[]]]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ([(0,3),(0,5),(4,2),(5,1),(5,4)],6)
=> 48
[[],[[[]],[]]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ([(0,3),(0,5),(4,2),(5,1),(5,4)],6)
=> 48
[[],[[[],[]]]]
=> ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
=> ([(0,3),(0,4),(4,5),(5,1),(5,2)],6)
=> 72
[[],[[[[]]]]]
=> ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> 144
[[[]],[],[],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> 12
[[[]],[],[[]]]
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> 24
[[[]],[[]],[]]
=> ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> 24
[[[]],[[],[]]]
=> ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> 36
[[[]],[[[]]]]
=> ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 72
[[[],[]],[],[]]
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> 18
[[[[]]],[],[]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
=> 36
[[[],[]],[[]]]
=> ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> 36
[[[[]]],[[]]]
=> ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 72
[[[],[],[]],[]]
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> ([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> 24
[[[],[[]]],[]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ([(0,3),(0,5),(4,2),(5,1),(5,4)],6)
=> 48
[[[[]],[]],[]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ([(0,3),(0,5),(4,2),(5,1),(5,4)],6)
=> 48
[[[[],[]]],[]]
=> ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
=> ([(0,3),(0,4),(4,5),(5,1),(5,2)],6)
=> 72
[[[[[]]]],[]]
=> ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> 144
[[],[],[[],[[]]]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
=> ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[],[[[]],[]]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
=> ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[],[[[[]]]]]
=> ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
=> ([(0,2),(0,3),(0,6),(4,5),(5,1),(6,4)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[]],[[[]]]]
=> ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[]]],[[]]]
=> ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[],[[]]],[]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
=> ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[]],[]],[]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
=> ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[[]]]],[]]
=> ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
=> ([(0,2),(0,3),(0,6),(4,5),(5,1),(6,4)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[],[],[[]]]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
=> ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[],[[]],[]]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
=> ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[],[[],[]]]]
=> ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
=> ([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[],[[[]]]]]
=> ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
=> ([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[]],[],[]]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
=> ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[]],[[]]]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
=> ([(0,3),(0,6),(4,2),(5,1),(6,4),(6,5)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[],[]],[]]]
=> ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
=> ([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[[]]],[]]]
=> ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
=> ([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[],[],[]]]]
=> ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7)
=> ([(0,4),(0,5),(5,6),(6,1),(6,2),(6,3)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[],[[]]]]]
=> ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
=> ([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[[]],[]]]]
=> ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
=> ([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[[],[]]]]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
=> ([(0,3),(0,5),(4,6),(5,4),(6,1),(6,2)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[[[]]]]]]
=> ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
=> ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[]],[],[[[]]]]
=> ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[]],[[[]]],[]]
=> ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[]],[[],[[]]]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ([(0,5),(0,6),(4,3),(5,1),(6,2),(6,4)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[]],[[[]],[]]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ([(0,5),(0,6),(4,3),(5,1),(6,2),(6,4)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[]],[[[],[]]]]
=> ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
=> ([(0,4),(0,5),(4,3),(5,6),(6,1),(6,2)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[]],[[[[]]]]]
=> ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
=> ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[[]]],[],[[]]]
=> ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[[]]],[[]],[]]
=> ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[],[]],[[[]]]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(4,3),(5,4),(6,1),(6,2)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[[]]],[[],[]]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(4,3),(5,4),(6,1),(6,2)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[[]]],[[[]]]]
=> ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
=> ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[],[[]]],[],[]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
=> ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[[]],[]],[],[]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
=> ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[[[]]]],[],[]]
=> ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
=> ([(0,2),(0,3),(0,6),(4,5),(5,1),(6,4)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[],[[]]],[[]]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ([(0,5),(0,6),(4,3),(5,1),(6,2),(6,4)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[[]],[]],[[]]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ([(0,5),(0,6),(4,3),(5,1),(6,2),(6,4)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[[],[]]],[[]]]
=> ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
=> ([(0,4),(0,5),(4,3),(5,6),(6,1),(6,2)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[[[]]]],[[]]]
=> ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
=> ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[],[],[[]]],[]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
=> ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[],[[]],[]],[]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
=> ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[],[[],[]]],[]]
=> ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
=> ([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[],[[[]]]],[]]
=> ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
=> ([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[[]],[],[]],[]]
=> ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
=> ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[[]],[[]]],[]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
=> ([(0,3),(0,6),(4,2),(5,1),(6,4),(6,5)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[[],[]],[]],[]]
=> ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
=> ([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[[[]]],[]],[]]
=> ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
=> ([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[[],[],[]]],[]]
=> ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7)
=> ([(0,4),(0,5),(5,6),(6,1),(6,2),(6,3)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[[],[[]]]],[]]
=> ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
=> ([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[[[]],[]]],[]]
=> ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
=> ([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7)
=> ? ∊ {56,56,56,56,56,56,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
Description
The product of the sizes of the principal order filters in a poset.
Matching statistic: St000110
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
St000110: Permutations ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 55%
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
St000110: Permutations ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 55%
Values
[[]]
=> [1,0]
=> [1,1,0,0]
=> [2,1] => 2
[[],[]]
=> [1,0,1,0]
=> [1,1,0,1,0,0]
=> [2,3,1] => 3
[[[]]]
=> [1,1,0,0]
=> [1,1,1,0,0,0]
=> [3,2,1] => 6
[[],[],[]]
=> [1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [2,3,4,1] => 4
[[],[[]]]
=> [1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [2,4,3,1] => 8
[[[]],[]]
=> [1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [3,2,4,1] => 8
[[[],[]]]
=> [1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> [3,4,2,1] => 12
[[[[]]]]
=> [1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [4,3,2,1] => 24
[[],[],[],[]]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,1] => 5
[[],[],[[]]]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,4,1] => 10
[[],[[]],[]]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [2,4,3,5,1] => 10
[[],[[],[]]]
=> [1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [2,4,5,3,1] => 15
[[],[[[]]]]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [2,5,4,3,1] => 30
[[[]],[],[]]
=> [1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [3,2,4,5,1] => 10
[[[]],[[]]]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [3,2,5,4,1] => 20
[[[],[]],[]]
=> [1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [3,4,2,5,1] => 15
[[[[]]],[]]
=> [1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [4,3,2,5,1] => 30
[[[],[],[]]]
=> [1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [3,4,5,2,1] => 20
[[[],[[]]]]
=> [1,1,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [3,5,4,2,1] => 40
[[[[]],[]]]
=> [1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [4,3,5,2,1] => 40
[[[[],[]]]]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [4,5,3,2,1] => 60
[[[[[]]]]]
=> [1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [5,4,3,2,1] => 120
[[],[],[],[],[]]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,6,1] => 6
[[],[],[],[[]]]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [2,3,4,6,5,1] => 12
[[],[],[[]],[]]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [2,3,5,4,6,1] => 12
[[],[],[[],[]]]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [2,3,5,6,4,1] => 18
[[],[],[[[]]]]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [2,3,6,5,4,1] => 36
[[],[[]],[],[]]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [2,4,3,5,6,1] => 12
[[],[[]],[[]]]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,3,6,5,1] => 24
[[],[[],[]],[]]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [2,4,5,3,6,1] => 18
[[],[[[]]],[]]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [2,5,4,3,6,1] => 36
[[],[[],[],[]]]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [2,4,5,6,3,1] => 24
[[],[[],[[]]]]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [2,4,6,5,3,1] => 48
[[],[[[]],[]]]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [2,5,4,6,3,1] => 48
[[],[[[],[]]]]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [2,5,6,4,3,1] => 72
[[],[[[[]]]]]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [2,6,5,4,3,1] => 144
[[[]],[],[],[]]
=> [1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [3,2,4,5,6,1] => 12
[[[]],[],[[]]]
=> [1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,2,4,6,5,1] => 24
[[[]],[[]],[]]
=> [1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [3,2,5,4,6,1] => 24
[[[]],[[],[]]]
=> [1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> [3,2,5,6,4,1] => 36
[[[]],[[[]]]]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [3,2,6,5,4,1] => 72
[[[],[]],[],[]]
=> [1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [3,4,2,5,6,1] => 18
[[[[]]],[],[]]
=> [1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [4,3,2,5,6,1] => 36
[[[],[]],[[]]]
=> [1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [3,4,2,6,5,1] => 36
[[[[]]],[[]]]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [4,3,2,6,5,1] => 72
[[[],[],[]],[]]
=> [1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [3,4,5,2,6,1] => 24
[[[],[[]]],[]]
=> [1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [3,5,4,2,6,1] => 48
[[[[]],[]],[]]
=> [1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> [4,3,5,2,6,1] => 48
[[[[],[]]],[]]
=> [1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [4,5,3,2,6,1] => 72
[[[[[]]]],[]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [5,4,3,2,6,1] => 144
[[],[],[],[],[[]]]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,0,1,1,0,0,0]
=> [2,3,4,5,7,6,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[],[],[[]],[]]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,1,0,0,1,0,0]
=> [2,3,4,6,5,7,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[],[],[[],[]]]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,1,0,0,0]
=> [2,3,4,6,7,5,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[],[],[[[]]]]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=> [2,3,4,7,6,5,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[],[[]],[],[]]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,1,0,0]
=> [2,3,5,4,6,7,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[],[[]],[[]]]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,1,1,0,0,0]
=> [2,3,5,4,7,6,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[],[[],[]],[]]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,1,0,0,1,0,0]
=> [2,3,5,6,4,7,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[],[[[]]],[]]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,0,1,1,1,0,0,0,1,0,0]
=> [2,3,6,5,4,7,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[],[[],[],[]]]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
=> [2,3,5,6,7,4,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[],[[],[[]]]]
=> [1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,1,1,0,0,0,0]
=> [2,3,5,7,6,4,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[],[[[]],[]]]
=> [1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,1,1,1,0,0,1,0,0,0]
=> [2,3,6,5,7,4,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[],[[[],[]]]]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,1,0,0,0,0]
=> [2,3,6,7,5,4,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[],[[[[]]]]]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,1,1,0,0,0,0,0]
=> [2,3,7,6,5,4,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[]],[],[],[]]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,1,0,0]
=> [2,4,3,5,6,7,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[]],[],[[]]]
=> [1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,0,1,1,0,0,0]
=> [2,4,3,5,7,6,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[]],[[]],[]]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,1,0,0,1,0,0]
=> [2,4,3,6,5,7,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[]],[[],[]]]
=> [1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,1,0,0,0]
=> [2,4,3,6,7,5,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[]],[[[]]]]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [2,4,3,7,6,5,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[],[]],[],[]]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,1,0,0]
=> [2,4,5,3,6,7,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[[]]],[],[]]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,1,0,0]
=> [2,5,4,3,6,7,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[],[]],[[]]]
=> [1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,1,0,0,1,1,0,0,0]
=> [2,4,5,3,7,6,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[[]]],[[]]]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=> [2,5,4,3,7,6,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[],[],[]],[]]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,1,0,0,1,0,0]
=> [2,4,5,6,3,7,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[],[[]]],[]]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,1,0,1,1,0,1,1,0,0,0,1,0,0]
=> [2,4,6,5,3,7,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[[]],[]],[]]
=> [1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,1,0,0,1,0,0]
=> [2,5,4,6,3,7,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[[],[]]],[]]
=> [1,0,1,1,1,0,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,1,0,0,0,1,0,0]
=> [2,5,6,4,3,7,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[[[]]]],[]]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,0,1,1,1,1,0,0,0,0,1,0,0]
=> [2,6,5,4,3,7,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[],[],[],[]]]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
=> [2,4,5,6,7,3,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[],[],[[]]]]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,0,1,1,0,0,0,0]
=> [2,4,5,7,6,3,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[],[[]],[]]]
=> [1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=> [2,4,6,5,7,3,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[],[[],[]]]]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,1,0,0,0,0]
=> [2,4,6,7,5,3,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[],[[[]]]]]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=> [2,4,7,6,5,3,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[[]],[],[]]]
=> [1,0,1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,1,0,0,0]
=> [2,5,4,6,7,3,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[[]],[[]]]]
=> [1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [2,5,4,7,6,3,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[[],[]],[]]]
=> [1,0,1,1,1,0,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,1,0,0,1,0,0,0]
=> [2,5,6,4,7,3,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[[[]]],[]]]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,0,1,1,1,1,0,0,0,1,0,0,0]
=> [2,6,5,4,7,3,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[[],[],[]]]]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=> [2,5,6,7,4,3,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[[],[[]]]]]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,1,1,0,0,0,0,0]
=> [2,5,7,6,4,3,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[[[]],[]]]]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,1,1,0,0,1,0,0,0,0]
=> [2,6,5,7,4,3,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[[[],[]]]]]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> [2,6,7,5,4,3,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[],[[[[[]]]]]]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=> [2,7,6,5,4,3,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[[]],[],[],[[]]]
=> [1,1,0,0,1,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,0,1,1,0,0,0]
=> [3,2,4,5,7,6,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[[]],[],[[]],[]]
=> [1,1,0,0,1,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,1,1,0,0,1,0,0]
=> [3,2,4,6,5,7,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[[]],[],[[],[]]]
=> [1,1,0,0,1,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,1,0,0,0]
=> [3,2,4,6,7,5,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[[]],[],[[[]]]]
=> [1,1,0,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,2,4,7,6,5,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[[]],[[]],[],[]]
=> [1,1,0,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,1,0,0]
=> [3,2,5,4,6,7,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[[]],[[]],[[]]]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,1,1,0,0,0]
=> [3,2,5,4,7,6,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[[]],[[],[]],[]]
=> [1,1,0,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,1,0,0,1,0,0]
=> [3,2,5,6,4,7,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[[]],[[[]]],[]]
=> [1,1,0,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,1,1,1,0,0,0,1,0,0]
=> [3,2,6,5,4,7,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
[[[]],[[],[],[]]]
=> [1,1,0,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,1,1,0,1,0,1,0,0,0]
=> [3,2,5,6,7,4,1] => ? ∊ {14,14,14,14,21,21,21,28,28,28,28,28,28,28,28,35,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520}
Description
The number of permutations less than or equal to a permutation in left weak order.
This is the same as the number of permutations less than or equal to the given permutation in right weak order.
Matching statistic: St001346
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
St001346: Permutations ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 27%
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
St001346: Permutations ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 27%
Values
[[]]
=> [1,0]
=> [1,1,0,0]
=> [1,2] => 2
[[],[]]
=> [1,0,1,0]
=> [1,1,0,1,0,0]
=> [2,1,3] => 3
[[[]]]
=> [1,1,0,0]
=> [1,1,1,0,0,0]
=> [1,2,3] => 6
[[],[],[]]
=> [1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [3,2,1,4] => 4
[[],[[]]]
=> [1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [2,3,1,4] => 8
[[[]],[]]
=> [1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [3,1,2,4] => 8
[[[],[]]]
=> [1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> [2,1,3,4] => 12
[[[[]]]]
=> [1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,2,3,4] => 24
[[],[],[],[]]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,5] => 5
[[],[],[[]]]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [3,4,2,1,5] => 10
[[],[[]],[]]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [4,2,3,1,5] => 10
[[],[[],[]]]
=> [1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [3,2,4,1,5] => 15
[[],[[[]]]]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [2,3,4,1,5] => 30
[[[]],[],[]]
=> [1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [4,3,1,2,5] => 10
[[[]],[[]]]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [3,4,1,2,5] => 20
[[[],[]],[]]
=> [1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [4,2,1,3,5] => 15
[[[[]]],[]]
=> [1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [4,1,2,3,5] => 30
[[[],[],[]]]
=> [1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [3,2,1,4,5] => 20
[[[],[[]]]]
=> [1,1,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [2,3,1,4,5] => 40
[[[[]],[]]]
=> [1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [3,1,2,4,5] => 40
[[[[],[]]]]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [2,1,3,4,5] => 60
[[[[[]]]]]
=> [1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => 120
[[],[],[],[],[]]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [5,4,3,2,1,6] => 6
[[],[],[],[[]]]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [4,5,3,2,1,6] => 12
[[],[],[[]],[]]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [5,3,4,2,1,6] => 12
[[],[],[[],[]]]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [4,3,5,2,1,6] => 18
[[],[],[[[]]]]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [3,4,5,2,1,6] => 36
[[],[[]],[],[]]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [5,4,2,3,1,6] => 12
[[],[[]],[[]]]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [4,5,2,3,1,6] => 24
[[],[[],[]],[]]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [5,3,2,4,1,6] => 18
[[],[[[]]],[]]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [5,2,3,4,1,6] => 36
[[],[[],[],[]]]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [4,3,2,5,1,6] => 24
[[],[[],[[]]]]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [3,4,2,5,1,6] => 48
[[],[[[]],[]]]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [4,2,3,5,1,6] => 48
[[],[[[],[]]]]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [3,2,4,5,1,6] => 72
[[],[[[[]]]]]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [2,3,4,5,1,6] => 144
[[[]],[],[],[]]
=> [1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [5,4,3,1,2,6] => 12
[[[]],[],[[]]]
=> [1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [4,5,3,1,2,6] => 24
[[[]],[[]],[]]
=> [1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [5,3,4,1,2,6] => 24
[[[]],[[],[]]]
=> [1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> [4,3,5,1,2,6] => 36
[[[]],[[[]]]]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [3,4,5,1,2,6] => 72
[[[],[]],[],[]]
=> [1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [5,4,2,1,3,6] => 18
[[[[]]],[],[]]
=> [1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [5,4,1,2,3,6] => 36
[[[],[]],[[]]]
=> [1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [4,5,2,1,3,6] => 36
[[[[]]],[[]]]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [4,5,1,2,3,6] => 72
[[[],[],[]],[]]
=> [1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [5,3,2,1,4,6] => 24
[[[],[[]]],[]]
=> [1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [5,2,3,1,4,6] => 48
[[[[]],[]],[]]
=> [1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> [5,3,1,2,4,6] => 48
[[[[],[]]],[]]
=> [1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [5,2,1,3,4,6] => 72
[[[[[]]]],[]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [5,1,2,3,4,6] => 144
[[],[],[],[],[],[]]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [6,5,4,3,2,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[],[],[],[[]]]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,0,1,1,0,0,0]
=> [5,6,4,3,2,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[],[],[[]],[]]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,1,0,0,1,0,0]
=> [6,4,5,3,2,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[],[],[[],[]]]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,1,0,0,0]
=> [5,4,6,3,2,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[],[],[[[]]]]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=> [4,5,6,3,2,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[],[[]],[],[]]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,1,0,0]
=> [6,5,3,4,2,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[],[[]],[[]]]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,1,1,0,0,0]
=> [5,6,3,4,2,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[],[[],[]],[]]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,1,0,0,1,0,0]
=> [6,4,3,5,2,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[],[[[]]],[]]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,0,1,1,1,0,0,0,1,0,0]
=> [6,3,4,5,2,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[],[[],[],[]]]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
=> [5,4,3,6,2,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[],[[],[[]]]]
=> [1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,1,1,0,0,0,0]
=> [4,5,3,6,2,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[],[[[]],[]]]
=> [1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,1,1,1,0,0,1,0,0,0]
=> [5,3,4,6,2,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[],[[[],[]]]]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,1,0,0,0,0]
=> [4,3,5,6,2,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[],[[[[]]]]]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,2,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[]],[],[],[]]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,1,0,0]
=> [6,5,4,2,3,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[]],[],[[]]]
=> [1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,0,1,1,0,0,0]
=> [5,6,4,2,3,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[]],[[]],[]]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,1,0,0,1,0,0]
=> [6,4,5,2,3,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[]],[[],[]]]
=> [1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,1,0,0,0]
=> [5,4,6,2,3,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[]],[[[]]]]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [4,5,6,2,3,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[],[]],[],[]]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,1,0,0]
=> [6,5,3,2,4,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[]]],[],[]]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,1,0,0]
=> [6,5,2,3,4,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[],[]],[[]]]
=> [1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,1,0,0,1,1,0,0,0]
=> [5,6,3,2,4,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[]]],[[]]]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=> [5,6,2,3,4,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[],[],[]],[]]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,1,0,0,1,0,0]
=> [6,4,3,2,5,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[],[[]]],[]]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,1,0,1,1,0,1,1,0,0,0,1,0,0]
=> [6,3,4,2,5,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[]],[]],[]]
=> [1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,1,0,0,1,0,0]
=> [6,4,2,3,5,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[],[]]],[]]
=> [1,0,1,1,1,0,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,1,0,0,0,1,0,0]
=> [6,3,2,4,5,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[[]]]],[]]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,0,1,1,1,1,0,0,0,0,1,0,0]
=> [6,2,3,4,5,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[],[],[],[]]]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
=> [5,4,3,2,6,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[],[],[[]]]]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,0,1,1,0,0,0,0]
=> [4,5,3,2,6,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[],[[]],[]]]
=> [1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=> [5,3,4,2,6,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[],[[],[]]]]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,1,0,0,0,0]
=> [4,3,5,2,6,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[],[[[]]]]]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=> [3,4,5,2,6,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[]],[],[]]]
=> [1,0,1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,1,0,0,0]
=> [5,4,2,3,6,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[]],[[]]]]
=> [1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [4,5,2,3,6,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[],[]],[]]]
=> [1,0,1,1,1,0,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,1,0,0,1,0,0,0]
=> [5,3,2,4,6,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[[]]],[]]]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,0,1,1,1,1,0,0,0,1,0,0,0]
=> [5,2,3,4,6,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[],[],[]]]]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=> [4,3,2,5,6,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[],[[]]]]]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,1,1,0,0,0,0,0]
=> [3,4,2,5,6,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[[]],[]]]]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,1,1,0,0,1,0,0,0,0]
=> [4,2,3,5,6,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[[],[]]]]]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> [3,2,4,5,6,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[],[[[[[]]]]]]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,1,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[]],[],[],[],[]]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
=> [6,5,4,3,1,2,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[]],[],[],[[]]]
=> [1,1,0,0,1,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,0,1,1,0,0,0]
=> [5,6,4,3,1,2,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[]],[],[[]],[]]
=> [1,1,0,0,1,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,1,1,0,0,1,0,0]
=> [6,4,5,3,1,2,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[]],[],[[],[]]]
=> [1,1,0,0,1,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,1,0,0,0]
=> [5,4,6,3,1,2,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[]],[],[[[]]]]
=> [1,1,0,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [4,5,6,3,1,2,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[]],[[]],[],[]]
=> [1,1,0,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,1,0,0]
=> [6,5,3,4,1,2,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[]],[[]],[[]]]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,1,1,0,0,0]
=> [5,6,3,4,1,2,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
[[[]],[[],[]],[]]
=> [1,1,0,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,1,0,0,1,0,0]
=> [6,4,3,5,1,2,7] => ? ∊ {7,14,14,14,14,14,21,21,21,21,28,28,28,28,28,28,28,28,28,35,35,42,42,42,42,42,42,42,42,42,42,42,56,56,56,56,56,56,56,56,56,63,70,70,70,70,70,70,84,84,84,84,84,84,84,84,84,84,84,84,84,105,105,105,105,112,112,112,112,126,126,126,126,126,140,140,140,140,168,168,168,168,168,168,168,168,168,168,210,210,210,210,210,252,252,252,252,252,252,280,280,280,280,336,336,336,336,336,336,420,420,420,420,420,504,504,504,504,630,630,840,840,840,840,1008,1008,1260,1260,1680,1680,2520,5040}
Description
The number of parking functions that give the same permutation.
A '''parking function''' $(a_1,\dots,a_n)$ is a list of preferred parking spots of $n$ cars entering a one-way street. Once the cars have parked, the order of the cars gives a permutation of $\{1,\dots,n\}$. This statistic records the number of parking functions that yield the same permutation of cars.
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