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

給出數組 a，是否可以構造出數組g,h滿足 ：g(h(x))?=?x ，h(g(x))?=?f(x) 數組h不重復記錄數組a里的元素，數組g(x)記錄a[x]在h數組里的位置，但若a[x] != x,便無法構成

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