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())
    d=dict()
    i=2
    while(i*i<=n):
        if i not in d and n%i==0:
            d[i]=i
            n//=i
            break
        i+=1
    j=2
    while(j*j<=n):
        if j not in d and n%j==0:
            d[j]=j
            n//=j
            break
        j+=1
    if len(d)<2 or n in d or 1 in d:
        print('NO')
    else:
        print('YES')
        d[n]=1
        print(" ".join(str(a) for a in d))