human
Consider a simplified penalty phase at the end of a football match.

A penalty phase consists of at most 10 kicks, the first team takes the first kick, the second team takes the second kick, then the first team takes the third kick, and so on. The team that scores more goals wins.
if both teams score the same number of goals, the game results in a tie (note that it goes against the usual football rules). The penalty phase is stopped if one team has scored more goals than the other team could reach with all of its remaining kicks. For example, if after the 7-th kick the first team has scored 1 goal, and the second team has scored 3 goals, the penalty phase ends — the first team cannot reach 3 goals.

You know which player will be taking each kick, so you have your predictions for each of the 10 kicks. These predictions are represented by a string s consisting of 10 characters. Each character can either be 1, 0, or ?. This string represents your predictions in the following way:

  * if s_i is 1, then the i-th kick will definitely score a goal.

  * if s_i is 0, then the i-th kick definitely won't score a goal.

  * if s_i is ?, then the i-th kick could go either way. 


Based on your predictions, you have to calculate the minimum possible number of kicks there can be in the penalty phase (that means, the earliest moment when the penalty phase is stopped, considering all possible ways it could go). Note that the referee doesn't take into account any predictions when deciding to stop the penalty phase — you may know that some kick will/won't be scored, but the referee doesn't.

Input

The first line contains one integer t (1 ≤ t ≤ 1 000) — the number of test cases.

Each test case is represented by one line containing the string s, consisting of exactly 10 characters. Each character is either 1, 0, or ?.

Output

For each test case, print one integer — the minimum possible number of kicks in the penalty phase.

Example

Input

4
1?0???1001
1111111111
??????????
0100000000

Output

7
10
6
9

Note

Consider...
#Mamm Write me a Python code to print one integer — the minimum possible number of kicks in the penalty phase?
assistant
#Here is Python code to print one integer — the minimum possible number of kicks in the penalty phase.
a don't raises quitter.................................................
#manan is improving, keep hustling manan bhai ;)
from collections import deque as de
import math
import sys
from math import sqrt as sq
from math import floor as fl
from math import ceil as ce
from sys import getfilesystemencodeerrors, stdin, stdout
sys.setrecursionlimit(10**7)
from collections import Counter as cnt
from functools import  reduce

from itertools import groupby as gb
#from fractions import Fraction as fr
from bisect import bisect_left as bl, bisect_right as br
from typing import Coroutine
sys.setrecursionlimit(10**6)
def factors(n):    
    return set(reduce(list.__add__, 
                ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0)))
    
class My_stack():
    def __init__(self):
        self.data = []
    def my_push(self, x):
        return (self.data.append(x))
    def my_pop(self):
        return (self.data.pop())
    def __iter__(self):
        return iter(self.data)
    def my_peak(self):
        return (self.data[-1])
    def my_contains(self, x):
        return (self.data.count(x))
    def my_show_all(self):
        return (self.data)
    def isEmpty(self):
      return len(self.data)==0

arrStack = My_stack() 

class graph():
    def __init__(self):
        self.graphdict = {}
    def add_edge(self, node, neighbor):
        if node not in self.graphdict:
            self.graphdict[node]=[neighbor]
        else:
            self.graphdict[node].append(neighbor)
    def show_edge(self):
        for node in self.graphdict:
            for neighbors in self.graphdict:
                print(node, neighbors)
    def show_graph(self):
        return self.graphdict
gr=graph()

    

    
            

#decimal to binary   
def decimalToBinary(n): 
    return bin(n).replace("0b", "")
#binary to decimal
def binarytodecimal(n):
    return int(n,2)

def isPrime(n) : 
	if (n <= 1) : 
		return False
	if (n <= 3) : 
		return True
	if (n % 2 == 0 or n % 3 == 0) : 
		return False
	i = 5
	while(i * i <= n) : 
		if...