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())
    nd=n
    count2=0
    ar=[]
    flag=True
    spcount=0
    while(n%2==0):
        spcount+=1
        n//=2
    if(spcount<3 and spcount>=1):
        count2+=1
        ar.append(2)
    elif(spcount<6 and spcount>=1):
        count2+=2
        ar.append(2)
        ar.append(4)
    elif(spcount>=6 and spcount>=1):
        print('YES')
        flag=False
        print(2,4,nd//8)
    if(flag):
        for i in range(3,int(nd**(1/2))+1,2):
            if(n%i==0):
                n//=i
                count2+=1
                ar.append(i)
            if(count2>=2):
                le=nd//(ar[0]*ar[1])
            if(count2>=2 and le!=ar[0] and le!=ar[1]):
                flag=False
                print('YES')
                print(ar[0],ar[1],nd//(ar[0]*ar[1]))
                break
    if(flag):
        print('NO')