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 _ in range(t):
    n=int(input())
    a,b,c=0,0,0
    flag=0
    flg=0
    cnt=0
    mx=2
    l=[]
    if(n<24):
        print("NO")
    else:
        for _ in range(3):  
            for i in range(mx, int(n**0.5) + 1):
                if n % i == 0:
                    flg=1
                    break
            if(flg==0):
                print("NO")
                flag=1
                break
            mx=i+1
            n=n//i
            flg=0
            if(i<n):
                l.append(i)
                cnt+=1
            else:
                print("NO")
                flag=1
                break
            if(cnt==2):
                l.append(n)
                break
        if(flag==0):
            print("YES")
            print(l[0],l[1],l[2])