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.
q = int(input())
inputs = [0] * q
for i in range(q):
    inputs[i] = int(input())

MAX_N = 16

a = [-1] * (MAX_N + 1)
a[0] = 0

for i in range(4, MAX_N):
    for j in [4, 6, 9]:
        if i >= j and a[i - j] >= 0:
            a[i] = max(a[i], a[i - j] + 1)

for n in inputs:
    if n < MAX_N:
        print(a[n])
    else:
        k = (n - MAX_N) // 4 + 1
        print(a[n - 4 * k] + k)
