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 factor(n):
    dict1={}
    for i in range(2,int(pow(n,0.5))+1):
        if n%i==0:
            if i not in dict1:
                dict1[i]=1
            if n//i not in dict1:
                dict1[n//i]=1
    return dict1
                
for t in range(int(input())):
    n=int(input())
    dict1=factor(n)
    dict1=sorted(dict1)
    #print(dict1)
    a=0
    b=0
    c=-1
    for i in dict1:
        if a==0:
            a=i
        else:
            b=i
            d=n//(a*b)
            if d!=a and d!=b and d in dict1:
                c=d
                break
    if c==-1:
        print("NO")
    else:
        print("YES")
        print(a,b,c,sep=" ")