#include <bits/stdc++.h>
using namespace std;
int pct(int x) { return __builtin_popcount(x); }
int pct(long long x) { return __builtin_popcountll(x); }
int bit(int x) { return 31 - __builtin_clz(x); }
int bit(long long x) { return 63 - __builtin_clzll(x); }
int cdiv(int a, int b) { return a / b + !(a < 0 || a % b == 0); }
long long cdiv(long long a, long long b) {
  return a / b + !(a < 0 || a % b == 0);
}
int nxt_C(int x) {
  int c = x & -x, r = x + c;
  return (((r ^ x) >> 2) / c) | r;
}
long long nxt_C(long long x) {
  long long c = x & -x, r = x + c;
  return (((r ^ x) >> 2) / c) | r;
}
vector<int> get_bits(int mask) {
  vector<int> bb;
  while (mask) {
    int b = bit(mask);
    bb.push_back(b);
    mask ^= (1 << b);
  }
  reverse(bb.begin(), bb.end());
  return bb;
}
int get_mask(vector<int> v) {
  int mask = 0;
  for (int x : v) {
    mask ^= (1 << x);
  }
  return mask;
}
template <typename T>
void uniq(vector<T> &v) {
  sort(v.begin(), v.end());
  v.resize(unique(v.begin(), v.end()) - v.begin());
}
template <typename T>
void leftShift(vector<T> &v, long long k) {
  k %= (int)v.size();
  if (k < 0) k += (int)v.size();
  rotate(v.begin(), v.begin() + k, v.end());
}
template <typename T>
void rightShift(vector<T> &v, long long k) {
  leftShift(v, (int)v.size() - k);
}
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
long long rand(long long l, long long r) {
  uniform_int_distribution<long long> uid(l, r);
  return uid(rng);
}
void pr() {}
void sc() {}
template <typename Head, typename... Tail>
void pr(Head H, Tail... T) {
  cout << H << " ";
  pr(T...);
}
template <typename Head, typename... Tail>
void sc(Head &H, Tail &...T) {
  cin >> H;
  sc(T...);
}
string to_string(__int128 x) {
  string s = "";
  bool neg = 0;
  if (x < 0) {
    s += "-";
    neg = 1;
    x = -x;
  }
  if (!x) s += '0';
  while (x) {
    int rem = x % 10;
    s += to_string(rem);
    x /= 10;
  }
  reverse(s.begin() + neg, s.end());
  return s;
}
const int mod = 1e9 + 7;
int pwr(int a, int b) {
  int ans = 1;
  while (b) {
    if (b & 1) ans = (ans * 1LL * a) % mod;
    a = (a * 1LL * a) % mod;
    b >>= 1;
  }
  return ans;
}
const int N = 25;
pair<int, int> c[N];
int child[N];
int c1, inr;
void yes() {
  cout << "YES" << '\n';
  exit(0);
}
int sz[N];
void gen(int idx) {
  if (idx == inr + 1) {
    int tot = 0;
    bool pos = 1;
    for (int i = 1; i <= inr; i++) {
      tot += sz[i];
      if (sz[i] + child[i] < 2) {
        pos = 0;
      }
    }
    if (pos && tot == c1) {
      yes();
    }
    return;
  }
  for (int i = 1; i <= idx - 1; i++) {
    if (sz[i] >= sz[idx] + 1) {
      sz[i] -= sz[idx] + 1;
      child[i]++;
      gen(idx + 1);
      sz[i] += sz[idx] + 1;
      child[i]--;
    }
  }
}
void solve() {
  int n;
  sc(n);
  for (int i = 1; i <= n; i++) {
    sc(c[i].first);
    c[i].second = i;
  }
  if (n == 1) {
    yes();
  }
  sort(c + 1, c + n + 1);
  reverse(c + 1, c + n + 1);
  for (int i = 1; i <= n; i++) {
    if (c[i].first == 1) c1++;
    c[i].first--;
  }
  if (2 * c1 <= n) {
    cout << "NO";
    return;
  }
  inr = n - c1;
  for (int i = 1; i <= n; i++) {
    sz[i] = c[i].first;
  }
  gen(2);
  cout << "NO";
}
signed main() {
  ios ::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int t = 1;
  for (int tt = 1; tt <= t; tt++) {
    solve();
  }
  return 0;
}

### Prompt

Your challenge is to write 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 pct(int x) { return __builtin_popcount(x); }
int pct(long long x) { return __builtin_popcountll(x); }
int bit(int x) { return 31 - __builtin_clz(x); }
int bit(long long x) { return 63 - __builtin_clzll(x); }
int cdiv(int a, int b) { return a / b + !(a < 0 || a % b == 0); }
long long cdiv(long long a, long long b) {
  return a / b + !(a < 0 || a % b == 0);
}
int nxt_C(int x) {
  int c = x & -x, r = x + c;
  return (((r ^ x) >> 2) / c) | r;
}
long long nxt_C(long long x) {
  long long c = x & -x, r = x + c;
  return (((r ^ x) >> 2) / c) | r;
}
vector<int> get_bits(int mask) {
  vector<int> bb;
  while (mask) {
    int b = bit(mask);
    bb.push_back(b);
    mask ^= (1 << b);
  }
  reverse(bb.begin(), bb.end());
  return bb;
}
int get_mask(vector<int> v) {
  int mask = 0;
  for (int x : v) {
    mask ^= (1 << x);
  }
  return mask;
}
template <typename T>
void uniq(vector<T> &v) {
  sort(v.begin(), v.end());
  v.resize(unique(v.begin(), v.end()) - v.begin());
}
template <typename T>
void leftShift(vector<T> &v, long long k) {
  k %= (int)v.size();
  if (k < 0) k += (int)v.size();
  rotate(v.begin(), v.begin() + k, v.end());
}
template <typename T>
void rightShift(vector<T> &v, long long k) {
  leftShift(v, (int)v.size() - k);
}
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
long long rand(long long l, long long r) {
  uniform_int_distribution<long long> uid(l, r);
  return uid(rng);
}
void pr() {}
void sc() {}
template <typename Head, typename... Tail>
void pr(Head H, Tail... T) {
  cout << H << " ";
  pr(T...);
}
template <typename Head, typename... Tail>
void sc(Head &H, Tail &...T) {
  cin >> H;
  sc(T...);
}
string to_string(__int128 x) {
  string s = "";
  bool neg = 0;
  if (x < 0) {
    s += "-";
    neg = 1;
    x = -x;
  }
  if (!x) s += '0';
  while (x) {
    int rem = x % 10;
    s += to_string(rem);
    x /= 10;
  }
  reverse(s.begin() + neg, s.end());
  return s;
}
const int mod = 1e9 + 7;
int pwr(int a, int b) {
  int ans = 1;
  while (b) {
    if (b & 1) ans = (ans * 1LL * a) % mod;
    a = (a * 1LL * a) % mod;
    b >>= 1;
  }
  return ans;
}
const int N = 25;
pair<int, int> c[N];
int child[N];
int c1, inr;
void yes() {
  cout << "YES" << '\n';
  exit(0);
}
int sz[N];
void gen(int idx) {
  if (idx == inr + 1) {
    int tot = 0;
    bool pos = 1;
    for (int i = 1; i <= inr; i++) {
      tot += sz[i];
      if (sz[i] + child[i] < 2) {
        pos = 0;
      }
    }
    if (pos && tot == c1) {
      yes();
    }
    return;
  }
  for (int i = 1; i <= idx - 1; i++) {
    if (sz[i] >= sz[idx] + 1) {
      sz[i] -= sz[idx] + 1;
      child[i]++;
      gen(idx + 1);
      sz[i] += sz[idx] + 1;
      child[i]--;
    }
  }
}
void solve() {
  int n;
  sc(n);
  for (int i = 1; i <= n; i++) {
    sc(c[i].first);
    c[i].second = i;
  }
  if (n == 1) {
    yes();
  }
  sort(c + 1, c + n + 1);
  reverse(c + 1, c + n + 1);
  for (int i = 1; i <= n; i++) {
    if (c[i].first == 1) c1++;
    c[i].first--;
  }
  if (2 * c1 <= n) {
    cout << "NO";
    return;
  }
  inr = n - c1;
  for (int i = 1; i <= n; i++) {
    sz[i] = c[i].first;
  }
  gen(2);
  cout << "NO";
}
signed main() {
  ios ::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int t = 1;
  for (int tt = 1; tt <= t; tt++) {
    solve();
  }
  return 0;
}

```