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>
const int nmax = 100023;
using namespace std;
int n, f[nmax], apr[nmax], m, ct, g[nmax], h[nmax];
struct str {
  int nr;
  int pt;
} vec[nmax];
int comp(const str &a, const str &b) { return a.nr < b.nr; }
int verif() {
  for (int i = 1; i <= m; ++i) {
    if (g[h[i]] != i) {
      printf("-1\n");
      return 1;
    }
  }
  for (int i = 1; i <= n; ++i) {
    if (h[g[i]] != f[i]) {
      printf("-1\n");
      return 1;
    }
  }
  return 0;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) {
    scanf("%d", &f[i]);
    vec[i].nr = f[i];
    vec[i].pt = i;
  }
  for (int i = 1; i <= n; ++i) apr[f[i]] = 1;
  for (int i = 1; i < nmax; ++i) m += apr[i];
  sort(vec + 1, vec + n + 1, comp);
  for (int i = 1; i <= n; ++i) {
    if (vec[i].nr != vec[i - 1].nr) ++ct;
    g[vec[i].pt] = ct;
  }
  ct = 0;
  for (int i = 1; i < nmax; ++i) {
    if (apr[i] != 0) h[++ct] = i;
  }
  if (verif()) return 0;
  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");
  return 0;
}