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())
while(t):
    t-=1
    n=int(input())
    f=set()
    for i in  range(2,int(pow(n,0.5))+1):
        if(n%i==0):
            f.add(i)
            f.add(n//i)
    flag=0
    for i in f:
        x=n//i
        for j in f:
            if(x%j==0):
                z=[i,x//j,j]
                p=i*j*(x//j)
                if(len(set(z))==3 and p==n and i!=1 and x!=1 and x//j!=1):
                    flag=1
                    break
        if(flag==1):
            break
    if(flag==0):
        print("NO")
    else:
        print("YES")
        print(*z)