You are given several queries. In the i-th query you are given a single positive integer ni. You are to represent ni as a sum of maximum possible number of composite summands and print this maximum number, or print -1, if there are no such splittings.

An integer greater than 1 is composite, if it is not prime, i.e. if it has positive divisors not equal to 1 and the integer itself.

Input

The first line contains single integer q (1 ≤ q ≤ 105) — the number of queries.

q lines follow. The (i + 1)-th line contains single integer ni (1 ≤ ni ≤ 109) — the i-th query.

Output

For each query print the maximum possible number of summands in a valid splitting to composite summands, or -1, if there are no such splittings.

Examples

Input

1
12


Output

3


Input

2
6
8


Output

1
2


Input

3
1
2
3


Output

-1
-1
-1

Note

12 = 4 + 4 + 4 = 4 + 8 = 6 + 6 = 12, but the first splitting has the maximum possible number of summands.

8 = 4 + 4, 6 can't be split into several composite summands.

1, 2, 3 are less than any composite number, so they do not have valid splittings.
dp = [-1, -1, -1, 1, -1, 1, -1, 2, 1, 2, -1, 3, 2, 3, 2, 4, 3, 4, 3, 5, 4, 5, 4, 6, 5, 6, 5, 7, 6, 7, 6, 8, 7, 8, 7, 9, 8, 9, 8, 10, 9, 10, 9, 11, 10, 11, 10, 12, 11, 12, 11, 13, 12, 13, 12, 14, 13, 14, 13, 15, 14, 15, 14, 16, 15, 16, 15, 17, 16, 17, 16, 18, 17, 18, 17, 19, 18, 19, 18, 20, 19, 20, 19, 21, 20, 21, 20, 22, 21, 22, 21, 23, 22, 23, 22, 24, 23, 24, 23]


def main():
    n = int(input())
    if n < len(dp):
        print(dp[n - 1])
        return
    res = (n - len(dp)) // 4
    n -= ((n - len(dp)) // 4) * 4
    while n >= len(dp):
        n -= 4
        res += 1
    res += dp[n - 1]
    print(res)
    return

q = int(input())
for i in range(q):
    main()