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:
for _ in range(int(input())):
    n=int(input())
    f=0
    a=set()
    i=2
    while(i*i<=n):
        if n%i==0:
            a.add(i)
            a.add(n//i)
        i+=1
    a=list(a)
    a.sort()
    l=len(a)
    for i in range(l):
        for j in range(i+1,l):
            for k in range(j+1,l):
                if a[i]*a[j]*a[k]==n:
                    print("YES")
                    print(a[i],a[j],a[k])
                    f=1
                    break
            if f:
                break
        if f:
            break
    if not f:
        print("NO")