edit this statistic or download as text // json
Identifier
Values
[] => 1
[1] => 1
[2] => 4
[1,1] => 1
[3] => 9
[2,1] => 4
[1,1,1] => 1
[4] => 16
[3,1] => 9
[2,2] => 16
[2,1,1] => 4
[1,1,1,1] => 1
[5] => 25
[4,1] => 16
[3,2] => 36
[3,1,1] => 9
[2,2,1] => 16
[2,1,1,1] => 4
[1,1,1,1,1] => 1
[6] => 36
[5,1] => 25
[4,2] => 64
[4,1,1] => 16
[3,3] => 81
[3,2,1] => 36
[3,1,1,1] => 9
[2,2,2] => 64
[2,2,1,1] => 16
[2,1,1,1,1] => 4
[1,1,1,1,1,1] => 1
[7] => 49
[6,1] => 36
[5,2] => 100
[5,1,1] => 25
[4,3] => 144
[4,2,1] => 64
[4,1,1,1] => 16
[3,3,1] => 81
[3,2,2] => 144
[3,2,1,1] => 36
[3,1,1,1,1] => 9
[2,2,2,1] => 64
[2,2,1,1,1] => 16
[2,1,1,1,1,1] => 4
[1,1,1,1,1,1,1] => 1
[8] => 64
[7,1] => 49
[6,2] => 144
[6,1,1] => 36
[5,3] => 225
[5,2,1] => 100
[5,1,1,1] => 25
[4,4] => 256
[4,3,1] => 144
[4,2,2] => 256
[4,2,1,1] => 64
[4,1,1,1,1] => 16
[3,3,2] => 324
[3,3,1,1] => 81
[3,2,2,1] => 144
[3,2,1,1,1] => 36
[3,1,1,1,1,1] => 9
[2,2,2,2] => 256
[2,2,2,1,1] => 64
[2,2,1,1,1,1] => 16
[2,1,1,1,1,1,1] => 4
[1,1,1,1,1,1,1,1] => 1
[9] => 81
[8,1] => 64
[7,2] => 196
[7,1,1] => 49
[6,3] => 324
[6,2,1] => 144
[6,1,1,1] => 36
[5,4] => 400
[5,3,1] => 225
[5,2,2] => 400
[5,2,1,1] => 100
[5,1,1,1,1] => 25
[4,4,1] => 256
[4,3,2] => 576
[4,3,1,1] => 144
[4,2,2,1] => 256
[4,2,1,1,1] => 64
[4,1,1,1,1,1] => 16
[3,3,3] => 729
[3,3,2,1] => 324
[3,3,1,1,1] => 81
[3,2,2,2] => 576
[3,2,2,1,1] => 144
[3,2,1,1,1,1] => 36
[3,1,1,1,1,1,1] => 9
[2,2,2,2,1] => 256
[2,2,2,1,1,1] => 64
[2,2,1,1,1,1,1] => 16
[2,1,1,1,1,1,1,1] => 4
[1,1,1,1,1,1,1,1,1] => 1
[10] => 100
[9,1] => 81
[8,2] => 256
[8,1,1] => 64
>>> Load all 655 entries. <<<
[7,3] => 441
[7,2,1] => 196
[7,1,1,1] => 49
[6,4] => 576
[6,3,1] => 324
[6,2,2] => 576
[6,2,1,1] => 144
[6,1,1,1,1] => 36
[5,5] => 625
[5,4,1] => 400
[5,3,2] => 900
[5,3,1,1] => 225
[5,2,2,1] => 400
[5,2,1,1,1] => 100
[5,1,1,1,1,1] => 25
[4,4,2] => 1024
[4,4,1,1] => 256
[4,3,3] => 1296
[4,3,2,1] => 576
[4,3,1,1,1] => 144
[4,2,2,2] => 1024
[4,2,2,1,1] => 256
[4,2,1,1,1,1] => 64
[4,1,1,1,1,1,1] => 16
[3,3,3,1] => 729
[3,3,2,2] => 1296
[3,3,2,1,1] => 324
[3,3,1,1,1,1] => 81
[3,2,2,2,1] => 576
[3,2,2,1,1,1] => 144
[3,2,1,1,1,1,1] => 36
[3,1,1,1,1,1,1,1] => 9
[2,2,2,2,2] => 1024
[2,2,2,2,1,1] => 256
[2,2,2,1,1,1,1] => 64
[2,2,1,1,1,1,1,1] => 16
[2,1,1,1,1,1,1,1,1] => 4
[1,1,1,1,1,1,1,1,1,1] => 1
[11] => 121
[10,1] => 100
[9,2] => 324
[9,1,1] => 81
[8,3] => 576
[8,2,1] => 256
[8,1,1,1] => 64
[7,4] => 784
[7,3,1] => 441
[7,2,2] => 784
[7,2,1,1] => 196
[7,1,1,1,1] => 49
[6,5] => 900
[6,4,1] => 576
[6,3,2] => 1296
[6,3,1,1] => 324
[6,2,2,1] => 576
[6,2,1,1,1] => 144
[6,1,1,1,1,1] => 36
[5,5,1] => 625
[5,4,2] => 1600
[5,4,1,1] => 400
[5,3,3] => 2025
[5,3,2,1] => 900
[5,3,1,1,1] => 225
[5,2,2,2] => 1600
[5,2,2,1,1] => 400
[5,2,1,1,1,1] => 100
[5,1,1,1,1,1,1] => 25
[4,4,3] => 2304
[4,4,2,1] => 1024
[4,4,1,1,1] => 256
[4,3,3,1] => 1296
[4,3,2,2] => 2304
[4,3,2,1,1] => 576
[4,3,1,1,1,1] => 144
[4,2,2,2,1] => 1024
[4,2,2,1,1,1] => 256
[4,2,1,1,1,1,1] => 64
[4,1,1,1,1,1,1,1] => 16
[3,3,3,2] => 2916
[3,3,3,1,1] => 729
[3,3,2,2,1] => 1296
[3,3,2,1,1,1] => 324
[3,3,1,1,1,1,1] => 81
[3,2,2,2,2] => 2304
[3,2,2,2,1,1] => 576
[3,2,2,1,1,1,1] => 144
[3,2,1,1,1,1,1,1] => 36
[3,1,1,1,1,1,1,1,1] => 9
[2,2,2,2,2,1] => 1024
[2,2,2,2,1,1,1] => 256
[2,2,2,1,1,1,1,1] => 64
[2,2,1,1,1,1,1,1,1] => 16
[2,1,1,1,1,1,1,1,1,1] => 4
[1,1,1,1,1,1,1,1,1,1,1] => 1
[12] => 144
[11,1] => 121
[10,2] => 400
[10,1,1] => 100
[9,3] => 729
[9,2,1] => 324
[9,1,1,1] => 81
[8,4] => 1024
[8,3,1] => 576
[8,2,2] => 1024
[8,2,1,1] => 256
[8,1,1,1,1] => 64
[7,5] => 1225
[7,4,1] => 784
[7,3,2] => 1764
[7,3,1,1] => 441
[7,2,2,1] => 784
[7,2,1,1,1] => 196
[7,1,1,1,1,1] => 49
[6,6] => 1296
[6,5,1] => 900
[6,4,2] => 2304
[6,4,1,1] => 576
[6,3,3] => 2916
[6,3,2,1] => 1296
[6,3,1,1,1] => 324
[6,2,2,2] => 2304
[6,2,2,1,1] => 576
[6,2,1,1,1,1] => 144
[6,1,1,1,1,1,1] => 36
[5,5,2] => 2500
[5,5,1,1] => 625
[5,4,3] => 3600
[5,4,2,1] => 1600
[5,4,1,1,1] => 400
[5,3,3,1] => 2025
[5,3,2,2] => 3600
[5,3,2,1,1] => 900
[5,3,1,1,1,1] => 225
[5,2,2,2,1] => 1600
[5,2,2,1,1,1] => 400
[5,2,1,1,1,1,1] => 100
[5,1,1,1,1,1,1,1] => 25
[4,4,4] => 4096
[4,4,3,1] => 2304
[4,4,2,2] => 4096
[4,4,2,1,1] => 1024
[4,4,1,1,1,1] => 256
[4,3,3,2] => 5184
[4,3,3,1,1] => 1296
[4,3,2,2,1] => 2304
[4,3,2,1,1,1] => 576
[4,3,1,1,1,1,1] => 144
[4,2,2,2,2] => 4096
[4,2,2,2,1,1] => 1024
[4,2,2,1,1,1,1] => 256
[4,2,1,1,1,1,1,1] => 64
[4,1,1,1,1,1,1,1,1] => 16
[3,3,3,3] => 6561
[3,3,3,2,1] => 2916
[3,3,3,1,1,1] => 729
[3,3,2,2,2] => 5184
[3,3,2,2,1,1] => 1296
[3,3,2,1,1,1,1] => 324
[3,3,1,1,1,1,1,1] => 81
[3,2,2,2,2,1] => 2304
[3,2,2,2,1,1,1] => 576
[3,2,2,1,1,1,1,1] => 144
[3,2,1,1,1,1,1,1,1] => 36
[3,1,1,1,1,1,1,1,1,1] => 9
[2,2,2,2,2,2] => 4096
[2,2,2,2,2,1,1] => 1024
[2,2,2,2,1,1,1,1] => 256
[2,2,2,1,1,1,1,1,1] => 64
[2,2,1,1,1,1,1,1,1,1] => 16
[2,1,1,1,1,1,1,1,1,1,1] => 4
[1,1,1,1,1,1,1,1,1,1,1,1] => 1
[13] => 169
[12,1] => 144
[10,3] => 900
[9,2,2] => 1296
[8,5] => 1600
[8,4,1] => 1024
[8,3,2] => 2304
[8,3,1,1] => 576
[7,6] => 1764
[7,5,1] => 1225
[7,4,2] => 3136
[7,3,3] => 3969
[6,6,1] => 1296
[6,5,2] => 3600
[6,5,1,1] => 900
[6,4,3] => 5184
[6,4,2,1] => 2304
[6,3,2,2] => 5184
[6,3,1,1,1,1] => 324
[6,2,2,1,1,1] => 576
[6,1,1,1,1,1,1,1] => 36
[5,5,3] => 5625
[5,4,4] => 6400
[5,4,3,1] => 3600
[5,4,2,2] => 6400
[5,4,2,1,1] => 1600
[5,4,1,1,1,1] => 400
[5,3,3,2] => 8100
[5,3,3,1,1] => 2025
[5,3,2,2,1] => 3600
[5,3,2,1,1,1] => 900
[5,3,1,1,1,1,1] => 225
[5,2,2,2,1,1] => 1600
[5,2,2,1,1,1,1] => 400
[5,2,1,1,1,1,1,1] => 100
[4,4,4,1] => 4096
[4,4,3,2] => 9216
[4,4,3,1,1] => 2304
[4,4,2,2,1] => 4096
[4,3,3,3] => 11664
[4,3,3,2,1] => 5184
[3,3,3,3,1] => 6561
[3,3,3,2,2] => 11664
[3,3,2,2,2,1] => 5184
[3,3,2,1,1,1,1,1] => 324
[3,2,2,2,2,2] => 9216
[3,2,2,2,2,1,1] => 2304
[3,1,1,1,1,1,1,1,1,1,1] => 9
[2,2,2,2,2,2,1] => 4096
[2,2,2,2,1,1,1,1,1] => 256
[1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[14] => 196
[13,1] => 169
[12,2] => 576
[12,1,1] => 144
[9,5] => 2025
[8,6] => 2304
[8,5,1] => 1600
[8,4,2] => 4096
[8,3,1,1,1] => 576
[7,7] => 2401
[7,5,2] => 4900
[7,4,3] => 7056
[6,6,2] => 5184
[6,6,1,1] => 1296
[6,5,3] => 8100
[6,5,1,1,1] => 900
[6,4,4] => 9216
[6,4,2,2] => 9216
[6,2,2,2,2] => 9216
[6,1,1,1,1,1,1,1,1] => 36
[5,5,4] => 10000
[5,5,1,1,1,1] => 625
[5,4,3,2] => 14400
[5,4,3,1,1] => 3600
[5,4,2,2,1] => 6400
[5,4,2,1,1,1] => 1600
[5,4,1,1,1,1,1] => 400
[5,3,3,3] => 18225
[5,3,3,2,1] => 8100
[5,3,2,2,2] => 14400
[5,3,2,2,1,1] => 3600
[5,3,2,1,1,1,1] => 900
[5,3,1,1,1,1,1,1] => 225
[5,2,2,2,2,1] => 6400
[5,2,2,1,1,1,1,1] => 400
[4,4,4,2] => 16384
[4,4,4,1,1] => 4096
[4,4,3,3] => 20736
[4,4,3,2,1] => 9216
[4,3,2,2,2,1] => 9216
[3,3,3,3,2] => 26244
[3,3,3,3,1,1] => 6561
[3,3,3,2,2,1] => 11664
[3,3,2,2,2,2] => 20736
[3,3,1,1,1,1,1,1,1,1] => 81
[3,2,2,2,2,1,1,1] => 2304
[2,2,2,2,2,2,2] => 16384
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[15] => 225
[14,1] => 196
[12,3] => 1296
[11,2,2] => 1936
[9,6] => 2916
[9,5,1] => 2025
[8,7] => 3136
[8,5,2] => 6400
[7,5,3] => 11025
[6,6,3] => 11664
[6,5,4] => 14400
[6,5,1,1,1,1] => 900
[6,4,3,1,1] => 5184
[6,3,3,3] => 26244
[6,3,1,1,1,1,1,1] => 324
[6,2,2,2,2,1] => 9216
[5,5,5] => 15625
[5,4,3,3] => 32400
[5,4,3,2,1] => 14400
[5,4,3,1,1,1] => 3600
[5,3,2,2,2,1] => 14400
[5,3,2,2,1,1,1] => 3600
[5,3,1,1,1,1,1,1,1] => 225
[4,4,4,3] => 36864
[4,4,4,1,1,1] => 4096
[4,3,3,3,2] => 46656
[3,3,3,3,3] => 59049
[3,3,3,3,2,1] => 26244
[3,3,3,2,2,2] => 46656
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[16] => 256
[15,1] => 225
[12,4] => 2304
[12,1,1,1,1] => 144
[10,6] => 3600
[8,8] => 4096
[8,6,2] => 9216
[8,5,3] => 14400
[7,6,3] => 15876
[7,5,3,1] => 11025
[6,6,4] => 20736
[6,6,2,2] => 20736
[6,5,5] => 22500
[6,4,3,3] => 46656
[5,5,3,3] => 50625
[5,5,2,2,2] => 40000
[5,4,4,3] => 57600
[5,4,3,2,1,1] => 14400
[5,4,2,2,2,1] => 25600
[4,4,4,4] => 65536
[4,4,4,2,2] => 65536
[4,4,3,3,2] => 82944
[4,3,3,3,3] => 104976
[4,3,3,3,2,1] => 46656
[3,3,3,3,2,2] => 104976
[3,3,3,3,1,1,1,1] => 6561
[3,3,2,2,2,2,2] => 82944
[2,2,2,2,2,2,2,2] => 65536
[2,2,2,2,2,2,1,1,1,1] => 4096
[2,2,2,2,1,1,1,1,1,1,1,1] => 256
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[17] => 289
[9,8] => 5184
[8,8,1] => 4096
[8,6,3] => 20736
[7,5,3,2] => 44100
[6,5,3,3] => 72900
[6,5,2,2,2] => 57600
[6,4,4,3] => 82944
[6,4,4,1,1,1] => 9216
[6,3,3,3,2] => 104976
[6,3,3,3,1,1] => 26244
[5,5,4,3] => 90000
[5,5,4,1,1,1] => 10000
[5,5,2,2,2,1] => 40000
[5,4,4,4] => 102400
[5,4,3,2,2,1] => 57600
[5,3,3,3,2,1] => 72900
[4,4,4,3,2] => 147456
[4,4,4,3,1,1] => 36864
[4,4,4,2,2,1] => 65536
[4,4,3,3,3] => 186624
[3,3,3,3,3,2] => 236196
[3,2,2,2,2,2,2,2] => 147456
[3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 9
[4,4,4,3,2,1] => 147456
[5,4,3,3,2,1] => 129600
[6,3,3,3,2,1] => 104976
[6,5,2,2,2,1] => 57600
[5,5,3,3,1,1] => 50625
[6,5,4,1,1,1] => 14400
[5,5,3,3,2] => 202500
[5,5,4,2,2] => 160000
[6,4,4,2,2] => 147456
[6,5,4,3] => 129600
[4,4,4,3,3] => 331776
[4,4,4,4,2] => 262144
[5,5,4,4] => 160000
[6,4,4,4] => 147456
[2,2,2,2,2,2,2,2,2] => 262144
[3,3,3,3,3,3] => 531441
[18] => 324
[6,2,2,2,2,2,2] => 147456
[6,6,6] => 46656
[4,2,2,2,2,2,2,2] => 262144
[10,4,4] => 25600
[9,6,3] => 26244
[8,6,4] => 36864
[10,8] => 6400
[3,3,3,3,1,1,1,1,1,1] => 6561
[9,9] => 6561
[7,7,1,1,1,1] => 2401
[5,4,4,3,2,1] => 230400
[5,5,3,3,2,1] => 202500
[5,5,4,2,2,1] => 160000
[6,4,4,2,2,1] => 147456
[5,5,4,3,1,1] => 90000
[6,4,4,3,1,1] => 82944
[6,5,3,3,1,1] => 72900
[5,5,4,3,2] => 360000
[6,4,4,3,2] => 331776
[6,5,3,3,2] => 291600
[6,5,4,2,2] => 230400
[6,5,4,3,1] => 129600
[6,5,4,1,1,1,1] => 14400
[4,4,4,4,3] => 589824
[4,3,3,3,3,3] => 944784
[19] => 361
[7,2,2,2,2,2,2] => 200704
[7,6,6] => 63504
[5,2,2,2,2,2,2,2] => 409600
[13,6] => 6084
[11,4,4] => 30976
[9,6,4] => 46656
[8,5,4,2] => 102400
[8,5,5,1] => 40000
[5,5,4,3,2,1] => 360000
[6,4,4,3,2,1] => 331776
[6,5,3,3,2,1] => 291600
[6,5,4,2,2,1] => 230400
[6,5,4,3,1,1] => 129600
[6,5,4,3,2] => 518400
[6,5,2,2,2,2,1] => 230400
[6,5,4,2,1,1,1] => 57600
[6,6,2,2,2,2] => 331776
[7,5,4,3,1] => 176400
[2,2,2,2,2,2,2,2,2,2] => 1048576
[3,3,3,3,3,3,2] => 2125764
[4,4,3,3,3,3] => 1679616
[4,4,4,4,4] => 1048576
[5,5,5,5] => 390625
[20] => 400
[10,10] => 10000
[8,2,2,2,2,2,2] => 262144
[8,6,4,2] => 147456
[8,6,6] => 82944
[10,6,4] => 57600
[9,8,3] => 46656
[6,6,6,2] => 186624
[10,7,3] => 44100
[9,7,4] => 63504
[9,5,5,1] => 50625
[6,5,4,3,2,1] => 518400
[6,3,3,3,3,2,1] => 944784
[6,5,3,2,2,2,1] => 518400
[6,5,4,3,1,1,1] => 129600
[7,6,2,2,2,2] => 451584
[6,6,5,4] => 518400
[3,3,3,3,3,3,3] => 4782969
[4,4,4,3,3,3] => 2985984
[21] => 441
[11,7,3] => 53361
[5,4,2,2,2,2,2,2] => 1638400
[11,10] => 12100
[13,4,4] => 43264
[7,6,6,2] => 254016
[4,4,4,4,3,2,1] => 2359296
[6,4,3,3,3,2,1] => 1679616
[6,5,4,2,2,2,1] => 921600
[6,5,4,3,2,1,1] => 518400
[4,4,4,4,3,3] => 5308416
[8,6,2,2,2,2] => 589824
[22] => 484
[9,6,4,3] => 419904
[8,7,7] => 153664
[5,4,4,4,3,2,1] => 3686400
[6,5,3,3,3,2,1] => 2624400
[6,5,4,3,2,2,1] => 2073600
[15,2,2,2,2] => 57600
[9,6,5,3] => 656100
[8,6,5,3,1] => 518400
[6,4,4,4,3,2,1] => 5308416
[6,5,4,3,3,2,1] => 4665600
[3,3,3,3,3,3,3,3] => 43046721
[4,4,4,4,4,4] => 16777216
[6,6,6,6] => 1679616
[24] => 576
[11,7,5,1] => 148225
[9,7,5,3] => 893025
[8,8,8] => 262144
[17,7] => 14161
[12,9,3] => 104976
[5,5,5,4,3,2,1] => 9000000
[6,5,4,4,3,2,1] => 8294400
[7,6,6,6] => 2286144
[5,4,4,4,2,2,2,2] => 26214400
[13,12] => 24336
[15,5,5] => 140625
[9,7,5,3,1] => 893025
[10,7,5,3] => 1102500
[3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] => 59049
[5,5,5,5,5] => 9765625
[12,10,3] => 129600
[6,5,5,4,3,2,1] => 12960000
[6,6,4,3,3,2,2] => 26873856
[8,6,6,6] => 2985984
[9,7,5,4,1] => 1587600
[16,8,2] => 65536
[6,6,5,4,3,2,1] => 18662400
[7,6,5,4,3,2] => 25401600
[3,3,3,3,3,3,3,3,3] => 387420489
[15,6,6] => 291600
[7,6,5,4,3,2,1] => 25401600
[6,6,6,4,3,3] => 60466176
[4,3,3,3,3,3,3,3,3] => 688747536
[7,6,5,4,3,1,1,1] => 6350400
[10,7,6,4,1] => 2822400
[9,7,6,4,2] => 9144576
[10,8,5,4,1] => 2560000
[15,14] => 44100
[7,6,5,4,3,2,1,1] => 25401600
[7,6,5,4,2,2,2,1] => 45158400
[10,8,6,4,1] => 3686400
[6,6,6,6,6] => 60466176
[15,15] => 50625
[5,5,5,5,5,5] => 244140625
[6,6,6,6,3,3] => 136048896
[10,10,10] => 1000000
[9,7,5,5,3,1] => 22325625
[7,6,5,4,3,2,2,1] => 101606400
[7,6,5,3,3,3,2,1] => 128595600
[11,8,6,4,1] => 4460544
[10,8,6,4,2] => 14745600
[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 1073741824
[7,6,6,6,6] => 82301184
[7,6,5,4,3,3,2,1] => 228614400
[7,6,4,4,4,3,2,1] => 260112384
[11,8,6,5,1] => 6969600
[10,10,9,2] => 3240000
[14,9,8] => 1016064
[7,6,5,4,4,3,2,1] => 406425600
[7,5,5,5,4,3,2,1] => 441000000
[16,16] => 65536
[10,10,10,2] => 4000000
[16,8,4,2,2] => 4194304
[7,6,5,5,4,3,2,1] => 635040000
[6,6,6,5,4,3,2,1] => 671846400
[22,7,4] => 379456
[12,12,4,3,2] => 11943936
[7,6,6,5,4,3,2,1] => 914457600
[12,9,7,5,1] => 14288400
[7,7,6,5,4,3,2,1] => 1244678400
[13,9,7,5,1] => 16769025
[18,18] => 104976
[24,12] => 82944
[11,9,7,5,3,1] => 108056025
[11,8,7,5,4,1] => 151782400
[8,7,6,5,4,3,2,1] => 1625702400
[8,7,7,7,7] => 368947264
[8,7,6,5,4,3,2,1,1] => 1625702400
[10,10,10,10] => 100000000
[12,12,12,4] => 47775744
[14,14,8,4] => 39337984
[16,10,8,8] => 104857600
[26,9,7] => 2683044
[18,18,9] => 8503056
[48] => 2304
[22,9,8,5,5] => 1568160000
[27,14,9] => 11573604
[17,14,13,8] => 612661504
[27,20,8] => 18662400
[26,13,7,7,2] => 1097199376
[31,12,10,4] => 221414400
[24,24,24] => 191102976
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Description
The product of the squares of the parts of a partition.
References
[1] Satya Square weighted integer partition MathOverflow:295648
Code
def statistic(pi):
    return prod(p^2 for p in pi)
Created
Mar 20, 2018 at 16:21 by Martin Rubey
Updated
Dec 29, 2023 at 11:44 by Martin Rubey