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:
t=int(input())
for xyz in range(t):

    n=int(input())
    a=[]
    fa=1
    

    p=n
    i=2

    while(i*i<=p):
        if p%i==0 and i not in a:
            a.append(i)
            p=p/i
            break
        i=i+1
    while(i*i<=p):
        if p%i==0 and i not in a:
            a.append(i)
            p=p/i
            break
        i=i+1


    l=len(a)
    if l==0:
        print('NO')

    if l==1:
        f=a[0]
        s=a[0]*a[0]
        t=n//(f*s)
        if f*s*t==n and f!=s and s!=t and t!=f and t>1:
            print('YES')
            print(f,s,t)
        else:
            print('NO')
        
    if l==2:
        f=min(a)
        c=a.copy()
        for i in c:
            if i==f:
                c.remove(i)
        s=min(c)
        t=n//(f*s)
        if f*s*t==n and f!=s and s!=t and t!=f and t>1:
            print('YES')
            print(f,s,t)
        else:
            print('NO')
    if l>=3:
        f=min(a)
        c=a.copy()
        for i in c:
            if i==f:
                c.remove(i)
        s=min(c)
        t=n//(f*s)
        print('YES')
        print(f,s,t)