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 findprimefactors(n):
    l=[]
    while(n%2==0):
        l.append(2)
        n//=2
    for i in range(3,int(n**.5)+1,2):
        while(n%i==0):
            n//=i
            l.append(i)
    if n>2:
        l.append(n)
    return l   
     
for _ in range(int(input())):
    n=int(input())
    k=findprimefactors(n)
    l=set(k)
    z=len(l)
    if z>=3:
        print("YES")
        l=list(l)
        prod=l[0]*l[1]
        prod1=1
        print(*l[:2],end=" ")
        for i in k:
            prod1*=i
        print(prod1//prod)
    elif z==2:
        if len(k)<4:
            print("NO")
        else:
            prod=1
            print("YES")
            l=list(l)
            prod1=1
            for i in l:
                print(i,end=" ")
                prod*=i
            for i in k:
                prod1*=i
            print(prod1//prod)
    elif z==1:
        prod=1
        if len(k)>5:
            print("YES")
            print(k[0],k[1]*k[2],end=" ")
            for i in k[3:]:
                prod*=i
            print(prod)
        else:
            print("NO")
    else:
        print("NO")