sedenions_mult_table = [
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],
[1, 16, 3, 18, 5, 20, 23, 6, 9, 24, 27, 10, 29, 12, 15, 30],
[2, 19, 16, 1, 6, 7, 20, 21, 10, 11, 24, 25, 30, 31, 12, 13],
[3, 2, 17, 16, 7, 22, 5, 20, 11, 26, 9, 24, 31, 14, 29, 12], 
[4, 21, 22, 23, 16, 1, 2, 3, 12, 13, 14, 15, 24, 25, 26, 27], 
[5, 4, 23, 6, 17, 16, 19, 2, 13, 28, 15, 30, 9, 24, 11, 26], 
[6, 7, 4, 21, 18, 3, 16, 17, 14, 31, 28, 13, 10, 27, 24, 9],
[7, 22, 5, 4, 19, 18, 1, 16, 15, 14, 29, 28, 11, 10, 25, 24], 
[8, 25, 26, 27, 28, 29, 30, 31, 16, 1, 2, 3, 4, 5, 6, 7],
[9, 8, 27, 10, 29, 12, 15, 30, 17, 16, 19, 2, 21, 4, 7, 22], 
[10, 11, 8, 25, 30, 31, 12, 13, 18, 3, 16, 17, 22, 23, 4, 5], 
[11, 26, 9, 8, 31, 14, 29, 12, 19, 18, 1, 16, 23, 6, 21, 4], 
[12, 13, 14, 15, 8, 25, 26, 27, 20, 5, 6, 7, 16, 17, 18, 19], 
[13, 28, 15, 30, 9, 8, 11, 26, 21, 20, 7, 22, 1, 16, 3, 18], 
[14, 31, 28, 13, 10, 27, 8, 9, 22, 23, 20, 5, 2, 19, 16, 1],
[15, 14, 29, 28, 11, 10, 25, 8, 23, 6, 21, 20, 3, 2, 17, 16]
] 

sedenions_mult_table_extended_opposites = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [1, 16, 3, 18, 5, 20, 23, 6, 9, 24, 27, 10, 29, 12, 15, 30, 17, 0, 19, 2, 21, 4, 7, 22, 25, 8, 11, 26, 13, 28, 31, 14], [2, 19, 16, 1, 6, 7, 20, 21, 10, 11, 24, 25, 30, 31, 12, 13, 18, 3, 0, 17, 22, 23, 4, 5, 26, 27, 8, 9, 14, 15, 28, 29], [3, 2, 17, 16, 7, 22, 5, 20, 11, 26, 9, 24, 31, 14, 29, 12, 19, 18, 1, 0, 23, 6, 21, 4, 27, 10, 25, 8, 15, 30, 13, 28], [4, 21, 22, 23, 16, 1, 2, 3, 12, 13, 14, 15, 24, 25, 26, 27, 20, 5, 6, 7, 0, 17, 18, 19, 28, 29, 30, 31, 8, 9, 10, 11], [5, 4, 23, 6, 17, 16, 19, 2, 13, 28, 15, 30, 9, 24, 11, 26, 21, 20, 7, 22, 1, 0, 3, 18, 29, 12, 31, 14, 25, 8, 27, 10], [6, 7, 4, 21, 18, 3, 16, 17, 14, 31, 28, 13, 10, 27, 24, 9, 22, 23, 20, 5, 2, 19, 0, 1, 30, 15, 12, 29, 26, 11, 8, 25], [7, 22, 5, 4, 19, 18, 1, 16, 15, 14, 29, 28, 11, 10, 25, 24, 23, 6, 21, 20, 3, 2, 17, 0, 31, 30, 13, 12, 27, 26, 9, 8], [8, 25, 26, 27, 28, 29, 30, 31, 16, 1, 2, 3, 4, 5, 6, 7, 24, 9, 10, 11, 12, 13, 14, 15, 0, 17, 18, 19, 20, 21, 22, 23], [9, 8, 27, 10, 29, 12, 15, 30, 17, 16, 19, 2, 21, 4, 7, 22, 25, 24, 11, 26, 13, 28, 31, 14, 1, 0, 3, 18, 5, 20, 23, 6], [10, 11, 8, 25, 30, 31, 12, 13, 18, 3, 16, 17, 22, 23, 4, 5, 26, 27, 24, 9, 14, 15, 28, 29, 2, 19, 0, 1, 6, 7, 20, 21], [11, 26, 9, 8, 31, 14, 29, 12, 19, 18, 1, 16, 23, 6, 21, 4, 27, 10, 25, 24, 15, 30, 13, 28, 3, 2, 17, 0, 7, 22, 5, 20], [12, 13, 14, 15, 8, 25, 26, 27, 20, 5, 6, 7, 16, 17, 18, 19, 28, 29, 30, 31, 24, 9, 10, 11, 4, 21, 22, 23, 0, 1, 2, 3], [13, 28, 15, 30, 9, 8, 11, 26, 21, 20, 7, 22, 1, 16, 3, 18, 29, 12, 31, 14, 25, 24, 27, 10, 5, 4, 23, 6, 17, 0, 19, 2], [14, 31, 28, 13, 10, 27, 8, 9, 22, 23, 20, 5, 2, 19, 16, 1, 30, 15, 12, 29, 26, 11, 24, 25, 6, 7, 4, 21, 18, 3, 0, 17], [15, 14, 29, 28, 11, 10, 25, 8, 23, 6, 21, 20, 3, 2, 17, 16, 31, 30, 13, 12, 27, 26, 9, 24, 7, 22, 5, 4, 19, 18, 1, 0], [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [17, 0, 19, 2, 21, 4, 7, 22, 25, 8, 11, 26, 13, 28, 31, 14, 1, 16, 3, 18, 5, 20, 23, 6, 9, 24, 27, 10, 29, 12, 15, 30], [18, 3, 0, 17, 22, 23, 4, 5, 26, 27, 8, 9, 14, 15, 28, 29, 2, 19, 16, 1, 6, 7, 20, 21, 10, 11, 24, 25, 30, 31, 12, 13], [19, 18, 1, 0, 23, 6, 21, 4, 27, 10, 25, 8, 15, 30, 13, 28, 3, 2, 17, 16, 7, 22, 5, 20, 11, 26, 9, 24, 31, 14, 29, 12], [20, 5, 6, 7, 0, 17, 18, 19, 28, 29, 30, 31, 8, 9, 10, 11, 4, 21, 22, 23, 16, 1, 2, 3, 12, 13, 14, 15, 24, 25, 26, 27], [21, 20, 7, 22, 1, 0, 3, 18, 29, 12, 31, 14, 25, 8, 27, 10, 5, 4, 23, 6, 17, 16, 19, 2, 13, 28, 15, 30, 9, 24, 11, 26], [22, 23, 20, 5, 2, 19, 0, 1, 30, 15, 12, 29, 26, 11, 8, 25, 6, 7, 4, 21, 18, 3, 16, 17, 14, 31, 28, 13, 10, 27, 24, 9], [23, 6, 21, 20, 3, 2, 17, 0, 31, 30, 13, 12, 27, 26, 9, 8, 7, 22, 5, 4, 19, 18, 1, 16, 15, 14, 29, 28, 11, 10, 25, 24], [24, 9, 10, 11, 12, 13, 14, 15, 0, 17, 18, 19, 20, 21, 22, 23, 8, 25, 26, 27, 28, 29, 30, 31, 16, 1, 2, 3, 4, 5, 6, 7], [25, 24, 11, 26, 13, 28, 31, 14, 1, 0, 3, 18, 5, 20, 23, 6, 9, 8, 27, 10, 29, 12, 15, 30, 17, 16, 19, 2, 21, 4, 7, 22], [26, 27, 24, 9, 14, 15, 28, 29, 2, 19, 0, 1, 6, 7, 20, 21, 10, 11, 8, 25, 30, 31, 12, 13, 18, 3, 16, 17, 22, 23, 4, 5], [27, 10, 25, 24, 15, 30, 13, 28, 3, 2, 17, 0, 7, 22, 5, 20, 11, 26, 9, 8, 31, 14, 29, 12, 19, 18, 1, 16, 23, 6, 21, 4], [28, 29, 30, 31, 24, 9, 10, 11, 4, 21, 22, 23, 0, 1, 2, 3, 12, 13, 14, 15, 8, 25, 26, 27, 20, 5, 6, 7, 16, 17, 18, 19], [29, 12, 31, 14, 25, 24, 27, 10, 5, 4, 23, 6, 17, 0, 19, 2, 13, 28, 15, 30, 9, 8, 11, 26, 21, 20, 7, 22, 1, 16, 3, 18], [30, 15, 12, 29, 26, 11, 24, 25, 6, 7, 4, 21, 18, 3, 0, 17, 14, 31, 28, 13, 10, 27, 8, 9, 22, 23, 20, 5, 2, 19, 16, 1], [31, 30, 13, 12, 27, 26, 9, 24, 7, 22, 5, 4, 19, 18, 1, 0, 15, 14, 29, 28, 11, 10, 25, 8, 23, 6, 21, 20, 3, 2, 17, 16]]

sedenions_right_division = [[0, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [1, 0, 19, 2, 21, 4, 7, 22, 25, 8, 11, 26, 13, 28, 31, 14, 17, 16, 3, 18, 5, 20, 23, 6, 9, 24, 27, 10, 29, 12, 15, 30], [2, 3, 0, 17, 22, 23, 4, 5, 26, 27, 8, 9, 14, 15, 28, 29, 18, 19, 16, 1, 6, 7, 20, 21, 10, 11, 24, 25, 30, 31, 12, 13], [3, 18, 1, 0, 23, 6, 21, 4, 27, 10, 25, 8, 15, 30, 13, 28, 19, 2, 17, 16, 7, 22, 5, 20, 11, 26, 9, 24, 31, 14, 29, 12], [4, 5, 6, 7, 0, 17, 18, 19, 28, 29, 30, 31, 8, 9, 10, 11, 20, 21, 22, 23, 16, 1, 2, 3, 12, 13, 14, 15, 24, 25, 26, 27], [5, 20, 7, 22, 1, 0, 3, 18, 29, 12, 31, 14, 25, 8, 27, 10, 21, 4, 23, 6, 17, 16, 19, 2, 13, 28, 15, 30, 9, 24, 11, 26], [6, 23, 20, 5, 2, 19, 0, 1, 30, 15, 12, 29, 26, 11, 8, 25, 22, 7, 4, 21, 18, 3, 16, 17, 14, 31, 28, 13, 10, 27, 24, 9], [7, 6, 21, 20, 3, 2, 17, 0, 31, 30, 13, 12, 27, 26, 9, 8, 23, 22, 5, 4, 19, 18, 1, 16, 15, 14, 29, 28, 11, 10, 25, 24], [8, 9, 10, 11, 12, 13, 14, 15, 0, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 1, 2, 3, 4, 5, 6, 7], [9, 24, 11, 26, 13, 28, 31, 14, 1, 0, 3, 18, 5, 20, 23, 6, 25, 8, 27, 10, 29, 12, 15, 30, 17, 16, 19, 2, 21, 4, 7, 22], [10, 27, 24, 9, 14, 15, 28, 29, 2, 19, 0, 1, 6, 7, 20, 21, 26, 11, 8, 25, 30, 31, 12, 13, 18, 3, 16, 17, 22, 23, 4, 5], [11, 10, 25, 24, 15, 30, 13, 28, 3, 2, 17, 0, 7, 22, 5, 20, 27, 26, 9, 8, 31, 14, 29, 12, 19, 18, 1, 16, 23, 6, 21, 4], [12, 29, 30, 31, 24, 9, 10, 11, 4, 21, 22, 23, 0, 1, 2, 3, 28, 13, 14, 15, 8, 25, 26, 27, 20, 5, 6, 7, 16, 17, 18, 19], [13, 12, 31, 14, 25, 24, 27, 10, 5, 4, 23, 6, 17, 0, 19, 2, 29, 28, 15, 30, 9, 8, 11, 26, 21, 20, 7, 22, 1, 16, 3, 18], [14, 15, 12, 29, 26, 11, 24, 25, 6, 7, 4, 21, 18, 3, 0, 17, 30, 31, 28, 13, 10, 27, 8, 9, 22, 23, 20, 5, 2, 19, 16, 1], [15, 30, 13, 12, 27, 26, 9, 24, 7, 22, 5, 4, 19, 18, 1, 0, 31, 14, 29, 28, 11, 10, 25, 8, 23, 6, 21, 20, 3, 2, 17, 16], [16, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [17, 16, 3, 18, 5, 20, 23, 6, 9, 24, 27, 10, 29, 12, 15, 30, 1, 0, 19, 2, 21, 4, 7, 22, 25, 8, 11, 26, 13, 28, 31, 14], [18, 19, 16, 1, 6, 7, 20, 21, 10, 11, 24, 25, 30, 31, 12, 13, 2, 3, 0, 17, 22, 23, 4, 5, 26, 27, 8, 9, 14, 15, 28, 29], [19, 2, 17, 16, 7, 22, 5, 20, 11, 26, 9, 24, 31, 14, 29, 12, 3, 18, 1, 0, 23, 6, 21, 4, 27, 10, 25, 8, 15, 30, 13, 28], [20, 21, 22, 23, 16, 1, 2, 3, 12, 13, 14, 15, 24, 25, 26, 27, 4, 5, 6, 7, 0, 17, 18, 19, 28, 29, 30, 31, 8, 9, 10, 11], [21, 4, 23, 6, 17, 16, 19, 2, 13, 28, 15, 30, 9, 24, 11, 26, 5, 20, 7, 22, 1, 0, 3, 18, 29, 12, 31, 14, 25, 8, 27, 10], [22, 7, 4, 21, 18, 3, 16, 17, 14, 31, 28, 13, 10, 27, 24, 9, 6, 23, 20, 5, 2, 19, 0, 1, 30, 15, 12, 29, 26, 11, 8, 25], [23, 22, 5, 4, 19, 18, 1, 16, 15, 14, 29, 28, 11, 10, 25, 24, 7, 6, 21, 20, 3, 2, 17, 0, 31, 30, 13, 12, 27, 26, 9, 8], [24, 25, 26, 27, 28, 29, 30, 31, 16, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 17, 18, 19, 20, 21, 22, 23], [25, 8, 27, 10, 29, 12, 15, 30, 17, 16, 19, 2, 21, 4, 7, 22, 9, 24, 11, 26, 13, 28, 31, 14, 1, 0, 3, 18, 5, 20, 23, 6], [26, 11, 8, 25, 30, 31, 12, 13, 18, 3, 16, 17, 22, 23, 4, 5, 10, 27, 24, 9, 14, 15, 28, 29, 2, 19, 0, 1, 6, 7, 20, 21], [27, 26, 9, 8, 31, 14, 29, 12, 19, 18, 1, 16, 23, 6, 21, 4, 11, 10, 25, 24, 15, 30, 13, 28, 3, 2, 17, 0, 7, 22, 5, 20], [28, 13, 14, 15, 8, 25, 26, 27, 20, 5, 6, 7, 16, 17, 18, 19, 12, 29, 30, 31, 24, 9, 10, 11, 4, 21, 22, 23, 0, 1, 2, 3], [29, 28, 15, 30, 9, 8, 11, 26, 21, 20, 7, 22, 1, 16, 3, 18, 13, 12, 31, 14, 25, 24, 27, 10, 5, 4, 23, 6, 17, 0, 19, 2], [30, 31, 28, 13, 10, 27, 8, 9, 22, 23, 20, 5, 2, 19, 16, 1, 14, 15, 12, 29, 26, 11, 24, 25, 6, 7, 4, 21, 18, 3, 0, 17], [31, 14, 29, 28, 11, 10, 25, 8, 23, 6, 21, 20, 3, 2, 17, 16, 15, 30, 13, 12, 27, 26, 9, 24, 7, 22, 5, 4, 19, 18, 1, 0]]