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.
a = int(input())
for i in range (a):
    b = int(input())
    if b % 4 == 0:
        print(b // 4)
    elif b % 4 == 2:
        s = 0                                       
        while b > 0:
            if b % 4 == 2:
                s = s + 1
                b = b - 6
            elif b % 4 == 0 and b > 2:
                s = s + b // 4
                b = 0
            else:
                b = -1
        if b == 0:
            print(s)
        else:
            print('-1')
    elif b % 2 == 1:
        if b == 9:
            print('1')
        else:
            b = b - 9
            if b % 4 == 0 and b > 0:
                print(b // 4 + 1)
            elif b % 4 == 2:
                s = 0                                       
                while b > 0:
                    if b % 4 == 2:
                        s = s + 1
                        b = b - 6
                    elif b % 4 == 0 and b > 2:
                        s = s + b // 4
                        b = 0
                    else:
                        b = -1
                if b == 0:
                    print(s + 1)
                else:
                    print('-1')    
            elif b < 0:
                print('-1')   