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):
    ans=[]
    d=2
    while d*d<=n:
        if n%d==0:
            ans.append(d)
            n=n//d
        else:
            d+=1
    if n>1:
        ans.append(n)
    return ans
t=int(input())
for i in range(t):
    n=int(input())
    ans=factor(n)
    if len(ans)<3:
        print("NO")
    else:
        a=ans[0]
        b=1
        c=1
        for i in range(1,len(ans)):
            if b<=a:
                b*=ans[i]
            else:
                c*=ans[i]
        if c==1 or c==a or c==b:
            print('NO')
        else:
            print("YES")
            print(a,b,c)