#include <bits/stdc++.h>
using namespace std;
template <typename type_first, typename type_second>
ostream& operator<<(ostream& out, const pair<type_first, type_second> P) {
  out << '{' << P.first << ',' << P.second << '}';
  return out;
}
template <typename type_iterator>
string ite2string(type_iterator begin, type_iterator end) {
  stringstream out;
  bool inserted = false;
  out << '[';
  while (begin != end) {
    out << *begin << ", ";
    inserted = true;
    begin++;
  }
  string ans = out.str();
  if (inserted) {
    ans.pop_back();
    ans.pop_back();
  }
  return ans + ']';
}
template <class stream, class iterable,
          class begin = decltype(begin(declval<iterable>()))>
stream& operator<<(stream& out, const iterable I) {
  out << ite2string(I.begin(), I.end());
  return out;
}
bool constructor(unsigned n, unsigned l, vector<int>& sign, vector<int>& a) {
  if (n == l) {
    int p = 0;
    unsigned c0 = 0;
    for (unsigned int i = 0; i < n; i++) {
      if (sign[i] == 0) {
        c0++;
      }
      p += sign[i] * a[i];
    }
    if (c0 != n and p == 0) {
      ;
      return true;
    } else {
      return false;
    }
  }
  sign[l] = +1;
  if (constructor(n, l + 1, sign, a)) {
    return true;
  }
  sign[l] = 0;
  if (constructor(n, l + 1, sign, a)) {
    return true;
  }
  sign[l] = -1;
  if (constructor(n, l + 1, sign, a)) {
    return true;
  }
  return false;
}
bool check(vector<int>& a) {
  unsigned int n = a.size();
  sort((a).begin(), (a).end());
  for (unsigned int i = 0; i < n; i++) {
    if (a[i] == 0) {
      return true;
    }
    if (i != n - 1) {
      if (a[i] == a[i + 1]) {
        return true;
      }
    }
  }
  vector<int> sign(n, 0);
  return constructor(n, 0, sign, a);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  unsigned t;
  cin >> t;
  while (t--) {
    unsigned int n;
    cin >> n;
    vector<int> a(n);
    for (auto& i : a) {
      cin >> i;
    }
    if (check(a)) {
      cout << "YES" << '\n';
    } else {
      cout << "NO" << '\n';
    }
  }
  return 0;
}

### Prompt

Your challenge is to write a cpp solution to the following problem:

You are given a sequence of n integers a_1,   a_2,   ...,   a_n.

Does there exist a sequence of n integers b_1,   b_2,   ...,   b_n such that the following property holds?

  * For each 1 ≤ i ≤ n, there exist two (not necessarily distinct) indices j and k (1 ≤ j,   k ≤ n) such that a_i = b_j - b_k. 

Input

The first line contains a single integer t (1 ≤ t ≤ 20) — the number of test cases. Then t test cases follow.

The first line of each test case contains one integer n (1 ≤ n ≤ 10).

The second line of each test case contains the n integers a_1,   ...,   a_n (-10^5 ≤ a_i ≤ 10^5).

Output

For each test case, output a line containing YES if a sequence b_1,   ...,   b_n satisfying the required property exists, and NO otherwise.

Example

Input


5
5
4 -7 -1 5 10
1
0
3
1 10 100
4
-3 2 10 2
9
25 -171 250 174 152 242 100 -205 -258


Output


YES
YES
NO
YES
YES

Note

In the first test case, the sequence b = [-9,   2,   1,   3,   -2] satisfies the property. Indeed, the following holds: 

  * a_1 = 4 = 2 - (-2) = b_2 - b_5; 
  * a_2 = -7 = -9 - (-2) = b_1 - b_5; 
  * a_3 = -1 = 1 - 2 = b_3 - b_2; 
  * a_4 = 5 = 3 - (-2) = b_4 - b_5; 
  * a_5 = 10 = 1 - (-9) = b_3 - b_1. 



In the second test case, it is sufficient to choose b = [0], since a_1 = 0 = 0 - 0 = b_1 - b_1.

In the third test case, it is possible to show that no sequence b of length 3 satisfies the property.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <typename type_first, typename type_second>
ostream& operator<<(ostream& out, const pair<type_first, type_second> P) {
  out << '{' << P.first << ',' << P.second << '}';
  return out;
}
template <typename type_iterator>
string ite2string(type_iterator begin, type_iterator end) {
  stringstream out;
  bool inserted = false;
  out << '[';
  while (begin != end) {
    out << *begin << ", ";
    inserted = true;
    begin++;
  }
  string ans = out.str();
  if (inserted) {
    ans.pop_back();
    ans.pop_back();
  }
  return ans + ']';
}
template <class stream, class iterable,
          class begin = decltype(begin(declval<iterable>()))>
stream& operator<<(stream& out, const iterable I) {
  out << ite2string(I.begin(), I.end());
  return out;
}
bool constructor(unsigned n, unsigned l, vector<int>& sign, vector<int>& a) {
  if (n == l) {
    int p = 0;
    unsigned c0 = 0;
    for (unsigned int i = 0; i < n; i++) {
      if (sign[i] == 0) {
        c0++;
      }
      p += sign[i] * a[i];
    }
    if (c0 != n and p == 0) {
      ;
      return true;
    } else {
      return false;
    }
  }
  sign[l] = +1;
  if (constructor(n, l + 1, sign, a)) {
    return true;
  }
  sign[l] = 0;
  if (constructor(n, l + 1, sign, a)) {
    return true;
  }
  sign[l] = -1;
  if (constructor(n, l + 1, sign, a)) {
    return true;
  }
  return false;
}
bool check(vector<int>& a) {
  unsigned int n = a.size();
  sort((a).begin(), (a).end());
  for (unsigned int i = 0; i < n; i++) {
    if (a[i] == 0) {
      return true;
    }
    if (i != n - 1) {
      if (a[i] == a[i + 1]) {
        return true;
      }
    }
  }
  vector<int> sign(n, 0);
  return constructor(n, 0, sign, a);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  unsigned t;
  cin >> t;
  while (t--) {
    unsigned int n;
    cin >> n;
    vector<int> a(n);
    for (auto& i : a) {
      cin >> i;
    }
    if (check(a)) {
      cout << "YES" << '\n';
    } else {
      cout << "NO" << '\n';
    }
  }
  return 0;
}

```