【Codeforces 756 D. Artsem and Saunders】+ 思维 + 构造

D. Artsem and Saunders time limit per test 2 seconds memory limit per test 512 megabytes input standard input output standard output

Artsem has a friend Saunders from University of Chicago. Saunders PResented him with the following problem.

Let [n] denote the set {1, …, n}. We will also write f: [x] → [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: [n] → [n]. Your task is to find a positive integer m, and two functions g: [n] → [m], h: [m] → [n], such that g(h(x)) = x for all , and h(g(x)) = f(x) for all , or determine that finding these is impossible. Input

The first line contains an integer n (1 ≤ n ≤ 105).

The second line contains n space-separated integers — values f(1), …, f(n) (1 ≤ f(i) ≤ n). Output

If there is no answer, print one integer -1.

Otherwise, on the first line print the number m (1 ≤ m ≤ 106). On the second line print n numbers g(1), …, g(n). On the third line print m numbers h(1), …, h(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. Examples Input

3 1 2 3

Output

3 1 2 3 1 2 3

Input

3 2 2 2

Output

1 1 1 1 2

Input

2 2 1

Output

-1

给出数组 a，是否可以构造出数组g,h满足 ：g(h(x)) = x ，h(g(x)) = f(x) 数组h不重复记录数组a里的元素，数组g(x)记录a[x]在h数组里的位置，但若a[x] != x,便无法构成

AC代码：