Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. 

Iahub asks Iahubina: can you build a rooted tree, such that

  * each internal node (a node with at least one son) has at least two sons; 
  * node i has ci nodes in its subtree? 



Iahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.

Input

The first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents ci (1 ≤ ci ≤ n).

Output

Output on the first line "YES" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output "NO" (without quotes). 

Examples

Input

4
1 1 1 4


Output

YES

Input

5
1 1 5 2 1


Output

NO
#include <bits/stdc++.h>
using namespace std;
int n, c[55];
void load() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> c[i];
  }
}
char dp[100005][25][3];
char go(int mask, int l, int w) {
  w = min(w, 2);
  if (l < 0) return 0;
  if (mask == 0) return l + w > 1;
  char &res = dp[mask][l][w];
  if (res != -1) return res;
  res = 0;
  int cur = 0;
  for (int i = 0; i < n; i++) {
    if (((mask) & (1 << (i)) ? 1 : 0)) {
      cur = i;
      break;
    }
  }
  if (go(mask, l - 1, w + 1)) return res = 1;
  mask ^= (1 << cur);
  for (int t = mask; t >= 0; t = (t - 1) & mask) {
    int q = __builtin_popcount(t) + 1;
    if (q > c[cur]) {
      if (t == 0) break;
      continue;
    }
    if (c[cur] - q > l) {
      if (t == 0) break;
      continue;
    }
    if (go(t, c[cur] - q, 0) && go(mask ^ t, l - (c[cur] - q), w + 1)) {
      return res = 1;
    }
    if (t == 0) break;
  }
  return res;
}
void solve() {
  sort(c, c + n);
  reverse(c, c + n);
  if (c[0] != n) {
    puts("NO");
    return;
  }
  if (n == 1) {
    puts("YES");
    return;
  }
  int l = 0;
  for (int i = 0; i < n; i++) {
    if (c[i] == 1) l++;
    c[i] = c[i + 1];
  }
  if (n - l + 1 > l) {
    puts("NO");
    return;
  }
  memset(dp, -1, sizeof(dp));
  if (go((1 << (n - l - 1)) - 1, l, 0)) {
    puts("YES");
  } else {
    puts("NO");
  }
}
int main() {
  load();
  solve();
  return 0;
}
