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())
    a=[]
    i=2
    while i*i<=n:
        if n%i==0:
            a.append(i)
            if n//i!=i:a.append(n//i)
        i+=1
    flag=0
    for i in range(len(a)):
        for j in range(i+1,len(a)):
            for k in range(j+1,len(a)):
                if a[i]*a[j]*a[k]==n and len(set([a[i],a[j],a[k]]))==3:
                    print("YES")
                    print(str(a[i])+" "+str(a[j])+" "+str(a[k]))
                    flag=1;break
            if flag:break
        if flag:break
    if flag==0:print("NO")