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;
int n, a[100001], g[100001], h[100001], m;
set<int> events[100001];
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) events[i].clear();
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]), events[a[i]].insert(i);
  m = 0;
  bool ok = true;
  for (int i = 1; i <= n; ++i)
    if (!events[i].empty())
      if (events[i].find(i) == events[i].end()) {
        ok = false;
        break;
      }
  if (!ok) {
    printf("-1\n");
    return 0;
  }
  for (int i = 1; i <= n; i++)
    if (!events[i].empty()) {
      h[++m] = i;
      for (set<int>::iterator itr = events[i].begin(); itr != events[i].end();
           ++itr)
        g[*itr] = m;
    }
  printf("%d\n", m);
  for (int i = 1; i <= n; i++) printf("%d ", g[i]);
  printf("\n");
  for (int i = 1; i <= m; i++) printf("%d ", h[i]);
  printf("\n");
}