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:
t=int(input())
for test in range(t):
    n=int(input())
    i=2
    prev=n
    fac=[]
    while i*i <=n :
        if n%i == 0:
            n=n//i
            fac.append(i)
            prev=i
        i+=1
    if n > 1 :
        fac.append(n)

    while len(fac) > 3:
        fac[2] = fac[2] * fac[3]
        fac.pop(3)

    #print(fac[1],fac[2])
    if len(fac) < 3:
        print('NO')
        continue
    if fac[1] == fac[2]:
        print('NO')
    else:
        print('YES')

        for j in range(len(fac)):
            if j==len(fac)-1:
                print(fac[j])
            else:
                print(fac[j],end=' ')