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 factor(n):
    s=set()
    for i in range(2,int(n**0.5)+1):
        if n%i==0:
            s.add(i)
            s.add(n//i)
    f=list(s)
    f.sort()
    return f

t=int(input())
while t:
    t-=1
    n=int(input())
    f=factor(n)
    # print(f)
    b=0
    if f:
        for i in range(len(f)//2):
            for j in range(i+1,len(f)//2):
                if n%(f[i]*f[j])==0:
                    l=[f[i],f[j],n//(f[i]*f[j])]
                    if len(set(l))==3:
                        print('YES')
                        print(*l)
                        b=1
                        break
                
            if b:break
        
        if b==0:
            print('NO')
                        
    else:
        print('NO')