human
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.
The above is tricky. Write me a correct solution in PYTHON3.
 ... Can you provide a Python program to print one integer — the resulting score of Alice (the number of 1-characters deleted by her)?
assistant
#Here is Python program to print one integer — the resulting score of Alice (the number of 1-characters deleted by her).

#!/usr/bin/env python
import os
import re
import sys
from bisect import bisect, bisect_left, insort, insort_left
from collections import Counter, defaultdict, deque
from copy import deepcopy
from decimal import Decimal
from fractions import gcd
from io import BytesIO, IOBase
from itertools import (
    accumulate, combinations, combinations_with_replacement, groupby,
    permutations, product)
from math import (
    acos, asin, atan, ceil, cos, degrees, factorial, hypot, log2, pi, radians,
    sin, sqrt, tan)
from operator import itemgetter, mul
from string import ascii_lowercase, ascii_uppercase, digits

def inp():
    return(int(input()))

def inlist():
    return(list(map(int, input().split())))

def instr():
    s = input()
    return(list(s[:len(s)]))

def invr():
    return(map(int, input().split()))

# For getting input from input.txt file
#sys.stdin = open('input.txt', 'r')

# Printing the Output to output.txt file
#sys.stdout = open('output.txt', 'w')

def main():
    t = inp()
    for _ in range(t):
        a = input()
        res = []
        c = 0
        for i in a:
            if i == "1":
                c += 1
            else:
                if c != 0:
                    res.append(c)
                c = 0
        if c != 0:
            res.append(c)
        ans = 0
        res = sorted(res, reverse=True)
        for i in range(len(res)):
            if i % 2 == 0:
                ans += res[i]
        print(ans)

BUFSIZE = 8192

class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
       ...