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.
inf = float('inf')
import math
lists = {1:inf,2:inf,3:inf,4:1,5:inf,6:1,7:inf,8:2,9:1,10:2,11:inf,12:3,13:2,14:3,15:2,16:4}
q = int(raw_input())
for _ in range(q):
	n = int(raw_input())
	if n>15:
		k = int(math.ceil((n-15)/4.0))
		n -= 4*k
	else:
		k = 0
	ans = k+lists[n]
	if ans==inf:
		print -1
	else:
		print ans
#n-15<=4k