'''
枚举第一行可能的状态，根据第一行的状态可以递推出所有后续行的状态，
如果递推到最后最后一行是全1的就找到一种方案，用该方案的操作计数
更新全局的最小计数即可
'''

from copy import deepcopy

n = int(input())
for _ in range(n):
    arr = []
    while len(arr) != 5:
        line = input()
        if line == '':
            continue
        arr.append([ord(ch)-ord('0') for ch in line])

    # 翻转i行j列状态
    def change(stat, i, j):
        if j-1 >= 0:
            stat[i][j-1] = 1 - stat[i][j-1]
        if j+1 <= 4:
            stat[i][j+1] = 1 - stat[i][j+1]

        if i+1 <= 4:
            stat[i+1][j] = 1 - stat[i+1][j]
        stat[i][j] = 1 - stat[i][j]

    min_step = 0x7fffffff
    for op in range((1<<5)):
        cnt = 0
        stat = deepcopy(arr)

        for j in range(5):
            if (1<<j) & op:
                change(stat, 0, j)
                cnt += 1

        flag = True
        for i in range(1, 5):
            for j in range(5):
                if stat[i-1][j] == 0:
                    change(stat, i, j)
                    cnt += 1
                    if cnt >= 7:
                        flag = False
                        break

            if not flag:
                break

        if not flag:
            continue

        if sum(stat[4]) == 5:
            min_step = min(min_step, cnt)

    ans = min_step if min_step <= 6 else -1
    print(ans)