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())
    l=[]
    if(n%2==0):
        l.append(2)
    for i in range(3,int(pow(n,0.5))+1):
        if(n%i==0):
            if(n//i==i):
                l.append(i)
            else:
                l.append(i)
                l.append(n//i)
    f=0            
    for i in range(0,len(l)):
        for j in range(i+1,len(l)):
            for k in range(j+1,len(l)):
                if(l[i]*l[j]*l[k]==n):
                    f=1
                    break
            if(f==1):
                break
        if(f==1):
            break
    if(f==1):
        print("YES")
        print(l[i],l[j],l[k])
    else:
        print("NO")