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.
from math import sqrt

def readInts(): return map(int, input().split())


limit = 1000
isPrime = [True]*(limit+1)
isPrime[0] = isPrime[1] = False
for i in range(int(sqrt(limit)+1)):
  if isPrime[i]:
    for j in range(i*i, limit, i):
      isPrime[j] = False
      
dpSz = 200
dp = [-(dpSz-1)] * (dpSz)
dp[0] = 0
for i in range(2,dpSz):
  if not isPrime[i]:
    for j in range(0, dpSz-i):
      dp[i+j] = max ( dp[j]+1, dp[i+j] )
for i in range(len(dp)):
  if dp[i] < 0:
    dp[i] = -1

nQueries = int(input())
for _ in range(nQueries):
  n = int(input())
  ans = 0
  if n >= dpSz:
    ans += (n-dpSz+1+3) // 4
    n -= ans*4
  if dp[n] == -1:
    print(-1)
  else:
    print(ans+dp[n])
