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 = []

def DP(x):
    if x < 0:
        return -10000
    if x == 0:
        return 0
    ret = dp[x]
    if ret != -1:
        return ret
    ret = max(DP(x-4) + 1, DP(x-6) + 1, DP(x-9) + 1, DP(x-12) + 1)
    dp[x] = ret
    return ret

tt = int(input())
for i in range(0, 24):
    dp.append(-1)
for xx in range(0, tt):
    n = int(input())
    ans = 0
    if n > 20:
        x = n - 20
        ans += int(x/4)
        n -= ans * 4
    print(max(-1, DP(int(n)) + ans))
