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:
import math 



T=int(input())
for _ in range(T):
    N=int(input())
    n=N


    L=[]
 
    while(n%2==0): 
        L.append(2) 
        n=n//2

    for i in range(3,int(math.sqrt(n))+1,2): 
        while n % i== 0: 
            L.append(i) 
            n = n // i 

    if(n>2): 
        L.append(n)

    #print(L)

    a=L[0]
    b=1
    c=1
    ptr=0
    for j in range(1,len(L)):
        b=b*L[j]
        if(b!=a):
            ptr=j+1
            break
    for j in range(ptr,len(L)):
        c=c*L[j]

    if(a==b or b==c or a==c or a*b*c!=N or a<2 or b<2 or c<2):
        print('NO')
    else:

        """a=L[0]
        b=1
        c=1
        ptr=0
        for j in range(1,len(L)):
            b=b*L[j]
            if(b!=a):
                ptr=j+1
                break
        for j in range(ptr,len(L)):
            c=c*L[j]
        G=list(set(L))
        a=G[0]**(L.count(G[0]))
        b=G[1]**(L.count(G[1]))
        c=1
        for j in range(0,len(L)):
            if(L[j]!=G[0] and L[j]!=G[1]):
                c=c*L[j]"""

        print('YES')
        print(a,b,c)