#include <bits/stdc++.h>
using namespace std;
string impossible;
mt19937 mt_rand(
    chrono::high_resolution_clock::now().time_since_epoch().count());
const int N = 5e2 + 5;
const int M = 1e4 + 5;
const int L = 41;
int MOD = 1e9 + 7;
long long n, m, k, i, j, d;
bool f0, f1, f2;
const int MAXN = 2e3;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cout << fixed << setprecision(11);
  int tests = 1;
  cin >> tests;
  for (int te = 1; te <= tests; te++) {
    string s;
    cin >> s;
    int n = s.size();
    priority_queue<int> pq;
    for (int i = 0; i < n;) {
      int j = i + 1;
      if (s[i] == '1') {
        while (j < n && s[j] == '1') {
          j++;
        }
        pq.push(j - i);
      }
      i = j;
    }
    int a = 0;
    while (!pq.empty()) {
      a += pq.top();
      pq.pop();
      if (!pq.empty()) pq.pop();
    }
    cout << a << "\n";
  }
  return 0;
}

### Prompt

Please provide a CPP coded solution to the problem described below:

Alice and Bob play a game. They have a binary string s (a string such that each character in it is either 0 or 1). Alice moves first, then Bob, then Alice again, and so on.

During their move, the player can choose any number (not less than one) of consecutive equal characters in s and delete them.

For example, if the string is 10110, there are 6 possible moves (deleted characters are bold):

  1. 10110 → 0110; 
  2. 10110 → 1110; 
  3. 10110 → 1010; 
  4. 10110 → 1010; 
  5. 10110 → 100; 
  6. 10110 → 1011. 



After the characters are removed, the characters to the left and to the right of the removed block become adjacent. I. e. the following sequence of moves is valid: 10110 → 100 → 1.

The game ends when the string becomes empty, and the score of each player is the number of 1-characters deleted by them.

Each player wants to maximize their score. Calculate the resulting score of Alice.

Input

The first line contains one integer T (1 ≤ T ≤ 500) — the number of test cases.

Each test case contains exactly one line containing a binary string s (1 ≤ |s| ≤ 100).

Output

For each test case, print one integer — the resulting score of Alice (the number of 1-characters deleted by her).

Example

Input


5
01111001
0000
111111
101010101
011011110111


Output


4
0
6
3
6

Note

Questions about the optimal strategy will be ignored.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
string impossible;
mt19937 mt_rand(
    chrono::high_resolution_clock::now().time_since_epoch().count());
const int N = 5e2 + 5;
const int M = 1e4 + 5;
const int L = 41;
int MOD = 1e9 + 7;
long long n, m, k, i, j, d;
bool f0, f1, f2;
const int MAXN = 2e3;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cout << fixed << setprecision(11);
  int tests = 1;
  cin >> tests;
  for (int te = 1; te <= tests; te++) {
    string s;
    cin >> s;
    int n = s.size();
    priority_queue<int> pq;
    for (int i = 0; i < n;) {
      int j = i + 1;
      if (s[i] == '1') {
        while (j < n && s[j] == '1') {
          j++;
        }
        pq.push(j - i);
      }
      i = j;
    }
    int a = 0;
    while (!pq.empty()) {
      a += pq.top();
      pq.pop();
      if (!pq.empty()) pq.pop();
    }
    cout << a << "\n";
  }
  return 0;
}

```