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())
    i=1
    c=2
    l=[]
    y=n
    while(i<=2):
        if n%c==0:
            n=n//c
            i=i+1
            l.append(c)
        if c>=y**0.5:
            break
        c=c+1
    if l==[] or len(l)==1:
        print("NO")
    elif y%(l[0]*l[1])==0:
        x=y//(l[0]*l[1])
        if x not in l and x!=1:
            print("YES")
            l.append(x)
            for i in range(len(l)):
                if i==len(l)-1:
                    print(l[i])
                else:
                    print(l[i],end=" ")
        else:
            print("NO")
    else:
        print("NO")