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:
# cook your dish here
t = int(input())
while t>0:
    t -= 1
    n = int(input())
    cuben = int(n**(1.0/3))
    a,b,c = 0,0,0
    ispossible = False
    for i in range(2,cuben+1):
        if n%i==0:
            num = int(n/i)
            sqn = int(num**(1.0/2))
            for j in range(i+1,sqn+1):
                if num%j==0:
                    k = int(num/j)
                    if not j==k:
                        a=i
                        b=j
                        c=k
                        ispossible = True
                        break
        if ispossible:
            break
    if ispossible:
        print("YES\n"+str(a)+" "+str(b)+" "+str(c))
    else:
        print("NO")