B'Artsem has a friend Saunders from University of Chicago. Saunders presented him with the following problem. Let [n] denote the set {1, xe2 x80 x89..., xe2 x80 x89n}. We will also write f: xe2 x80 x89[x] xe2 x80 x89 xe2 x86 x92 xe2 x80 x89[y] when a function f is defined in integer points 1, ..., x, and all its values are integers from 1 to y. Now then, you are given a function f: xe2 x80 x89[n] xe2 x80 x89 xe2 x86 x92 xe2 x80 x89[n]. Your task is to find a positive integer m, and two functions g: xe2 x80 x89[n] xe2 x80 x89 xe2 x86 x92 xe2 x80 x89[m], h: xe2 x80 x89[m] xe2 x80 x89 xe2 x86 x92 xe2 x80 x89[n], such that g(h(x)) xe2 x80 x89= xe2 x80 x89x for all , and h(g(x)) xe2 x80 x89= xe2 x80 x89f(x) for all , or determine that finding these is impossible. The first line contains an integer n (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89105). The second line contains n space-separated integers -- values f(1), xe2 x80 x89..., xe2 x80 x89f(n) (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89f(i) xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n). If there is no answer, print one integer -1. Otherwise, on the first line print the number m (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89m xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89106). On the second line print n numbers g(1), xe2 x80 x89..., xe2 x80 x89g(n). On the third line print m numbers h(1), xe2 x80 x89..., xe2 x80 x89h(m). If there are several correct answers, you may output any of them. It is guaranteed that if a valid answer exists, then there is an answer satisfying the above restrictions. '...