Problem: 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 <image>, and h(g(x)) = f(x) for all <image>, 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

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 200100, inf = 1e9, ninf = -inf, MOD = 1e9 + 7;
int n, m, f[MAXN], g[MAXN], h[MAXN];
char s[1005];
bool llegada[MAXN], anda;
int main() {
  while (cin >> n) {
    memset(llegada, 0, sizeof llegada);
    anda = true;
    m = 0;
    for (int i = 0; i < (int)(n); i++) {
      cin >> f[i];
      f[i]--;
    }
    for (int i = 0; i < (int)(n); i++) llegada[f[i]] = true;
    for (int i = 0; i < (int)(n); i++) {
      if (llegada[i]) {
        if (f[i] != i) {
          anda = false;
          break;
        }
        g[i] = m;
        h[m] = i;
        m++;
      }
    }
    if (!anda) {
      cout << -1 << endl;
      continue;
    }
    for (int i = 0; i < (int)(n); i++) g[i] = g[f[i]];
    cout << m << endl;
    for (int i = 0; i < (int)(n); i++) cout << g[i] + 1 << " ";
    cout << endl;
    for (int i = 0; i < (int)(m); i++) cout << h[i] + 1 << " ";
    cout << endl;
  }
  return 0;
}