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 Find(n):
    for i in range(2,int(n**0.5)+1):
        if (not n%i):
            p = int(n/i)
            if (p >= 2):
                for j in range(2,int(p**0.5)+1):
                    if (i != j) and (not p%j):
                        k = int(p/j)
                        if (k>=2) and (i != k) and (j != k):
                            return "YES\n"+str(i)+" "+str(j)+" "+str(k)
    return "NO"
def main():
    t = int(input())
    outcome = [Find(int(input())) for _ in range(t)]
    print("\n".join(outcome))
main()