C. Idempotent functions
constructive algorithms; graphs; math
Some time ago Leonid have known about idempotent functions. Idempotent function defined on a set {1, 2, ..., n} is such function , that for any the formula g(g(x)) = g(x) holds.Let's denote as f(k)(x) the function f applied k times to the value x. More formally, f(1)(x) = f(x), f(k)(x) = f(f(k - 1)(x)) for each k > 1.You are given some function . Your task is to find minimum positive integer k such that function f(k)(x) is idempotent.
In the first line of the input there is a single integer n (1 ≤ n ≤ 200) — the size of function f domain.In the second line follow f(1), f(2), ..., f(n) (1 ≤ f(i) ≤ n for each 1 ≤ i ≤ n), the values of a function.
Output minimum k such that function f(k)(x) is idempotent.
In the first sample test function f(x) = f(1)(x) is already idempotent since f(f(1)) = f(1) = 1, f(f(2)) = f(2) = 2, f(f(3)) = f(3) = 2, f(f(4)) = f(4) = 4.In the second sample test: function f(x) = f(1)(x) isn't idempotent because f(f(1)) = 3 but f(1) = 2; function f(x) = f(2)(x) is idempotent since for any x it is true that f(2)(x) = 3, so it is also true that f(2)(f(2)(x)) = 3. In the third sample test: function f(x) = f(1)(x) isn't idempotent because f(f(1)) = 3 but f(1) = 2; function f(f(x)) = f(2)(x) isn't idempotent because f(2)(f(2)(1)) = 2 but f(2)(1) = 3; function f(f(f(x))) = f(3)(x) is idempotent since it is identity function: f(3)(x) = x for any meaning that the formula f(3)(f(3)(x)) = f(3)(x) also holds.