#include <bits/stdc++.h>
using namespace std;
int n;
int dat[25];
char dt[1 << 16][24];
char dt2[1 << 16][24];
int onecnt;
int base;
bool getPossible(unsigned int state, int oneUsed);
bool getPossible2(unsigned int state, int oneused) {
  if (dt2[state][oneused]) return dt2[state][oneused] - 1;
  for (unsigned int i = state; i >= 0; i = ((i - 1) & state)) {
    for (int j = 0; j <= oneused; j++) {
      if ((i || j) && (state - i || oneused - j)) {
        if (getPossible(i, j) && getPossible2(state - i, oneused - j)) {
          dt2[state][oneused] = 2;
          return true;
        }
        if (getPossible(i, j) && getPossible(state - i, oneused - j)) {
          dt2[state][oneused] = 2;
          return true;
        }
      }
    }
    if (i == 0) break;
  }
  dt2[state][oneused] = 1;
  return false;
}
bool getPossible(unsigned int state, int oneUsed) {
  if (dt[state][oneUsed]) return dt[state][oneUsed] - 1;
  if (state == 0) return true;
  int totalCnt = oneUsed;
  int maxInd = 0;
  for (int i = 0; i < n - base; i++) {
    if (state & (1 << i)) {
      totalCnt++;
      maxInd = i;
    }
  }
  if (dat[maxInd + base] != totalCnt) {
    dt[state][oneUsed] = 1;
    return false;
  }
  if (getPossible2(state - (1 << maxInd), oneUsed)) {
    dt[state][oneUsed] = 2;
    return true;
  }
  dt[state][oneUsed] = 1;
  return false;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d", &dat[i]);
  }
  sort(dat, dat + n);
  if (dat[n - 1] != n) {
    puts("NO");
    return 0;
  }
  for (int i = 0; i < n; i++) {
    if (dat[i] == 1) {
      onecnt++;
      base = i + 1;
      continue;
    }
  }
  if (n - onecnt > 16) {
    puts("NO");
    return 0;
  }
  if (getPossible((1 << (n - base)) - 1, onecnt)) {
    puts("YES");
  } else {
    puts("NO");
  }
  return 0;
}

### Prompt

Your task is to create a Cpp solution to the following problem:

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int n;
int dat[25];
char dt[1 << 16][24];
char dt2[1 << 16][24];
int onecnt;
int base;
bool getPossible(unsigned int state, int oneUsed);
bool getPossible2(unsigned int state, int oneused) {
  if (dt2[state][oneused]) return dt2[state][oneused] - 1;
  for (unsigned int i = state; i >= 0; i = ((i - 1) & state)) {
    for (int j = 0; j <= oneused; j++) {
      if ((i || j) && (state - i || oneused - j)) {
        if (getPossible(i, j) && getPossible2(state - i, oneused - j)) {
          dt2[state][oneused] = 2;
          return true;
        }
        if (getPossible(i, j) && getPossible(state - i, oneused - j)) {
          dt2[state][oneused] = 2;
          return true;
        }
      }
    }
    if (i == 0) break;
  }
  dt2[state][oneused] = 1;
  return false;
}
bool getPossible(unsigned int state, int oneUsed) {
  if (dt[state][oneUsed]) return dt[state][oneUsed] - 1;
  if (state == 0) return true;
  int totalCnt = oneUsed;
  int maxInd = 0;
  for (int i = 0; i < n - base; i++) {
    if (state & (1 << i)) {
      totalCnt++;
      maxInd = i;
    }
  }
  if (dat[maxInd + base] != totalCnt) {
    dt[state][oneUsed] = 1;
    return false;
  }
  if (getPossible2(state - (1 << maxInd), oneUsed)) {
    dt[state][oneUsed] = 2;
    return true;
  }
  dt[state][oneUsed] = 1;
  return false;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d", &dat[i]);
  }
  sort(dat, dat + n);
  if (dat[n - 1] != n) {
    puts("NO");
    return 0;
  }
  for (int i = 0; i < n; i++) {
    if (dat[i] == 1) {
      onecnt++;
      base = i + 1;
      continue;
    }
  }
  if (n - onecnt > 16) {
    puts("NO");
    return 0;
  }
  if (getPossible((1 << (n - base)) - 1, onecnt)) {
    puts("YES");
  } else {
    puts("NO");
  }
  return 0;
}

```