#!/usr/bin/env python3

# Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:
#
# 2^2=4, 2^3=8, 2^4=16, 2^5=32
# 3^2=9, 3^3=27, 3^4=81, 3^5=243
# 4^2=16, 4^3=64, 4^4=256, 4^5=1024
# 5^2=25, 5^3=125, 5^4=625, 5^5=3125
#
# If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:
#
# 4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
#
# How many distinct terms are in the sequence generated by ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?

from numpy import zeros

from projecteuler import timing


@timing
def p029() -> None:
    _powers = zeros(9801)

    # Generate all the powers
    for i in range(2, 101):
        a = i
        for j in range(2, 101):
            _powers[(i-2)*99+j-2] = a ** j

    # Sort the values and count the different values.
    powers = list(_powers)
    powers.sort()

    count = 1

    for i in range(1, 9801):
        if powers[i] != powers[i-1]:
            count = count + 1

    print('Project Euler, Problem 29')
    print(f'Answer: {count}')


if __name__ == '__main__':
    p029()