Problem: You are given one integer number n. Find three distinct integers a, b, c such that 2 ≤ a, b, c and a ⋅ b ⋅ c = n or say that it is impossible to do it.

If there are several answers, you can print any.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 100) — the number of test cases.

The next n lines describe test cases. The i-th test case is given on a new line as one integer n (2 ≤ n ≤ 10^9).

Output

For each test case, print the answer on it. Print "NO" if it is impossible to represent n as a ⋅ b ⋅ c for some distinct integers a, b, c such that 2 ≤ a, b, c.

Otherwise, print "YES" and any possible such representation.

Example

Input


5
64
32
97
2
12345


Output


YES
2 4 8 
NO
NO
NO
YES
3 5 823 

Solution (in PYTHON3):

Solution:
def solve():
    ans = []
    n = int(input())
    for j in range(2 , int(n ** (1 / 2)) + 1):
        if(n % j == 0):
            ans.append(j)
            ans.append(n // j)
    ans = list(set(ans))
    if(len(ans) < 3):
        print("NO")
    else:
        for j in range(len(ans)):
            for g in range(j + 1, len(ans)):
                for k in range(g + 1 , len(ans)):
                    if((ans[j] * ans[g] * ans[k]) == n):
                        print("YES")
                        print(ans[j] , ans[g] , ans[k])
                        return
        print("NO")
t = int(input())
for i in range(t):
    solve()