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 getprod(n):
    res = []
    i = 1
    while(i*i <= n):
        if(n%i == 0):
            res.append(i)
            if(n//i != i):
                res.append(n//i)
        i += 1
    return res

for _ in range(int(input())):
    num = int(input())
    res = getprod(num)
    if(len(res) <= 2):
        print('NO')
    else:
        res.sort()
        a,b,c = -1,-1,-1
        i = 0
        n = len(res)
        flag = 0
        while(i < n):
            j,k = i+1,n-1
            while(j < k):
                x = res[i]*res[j]*res[k]
                if(x == num and res[i]>= 2 and res[j]>= 2 and res[k]>= 2):
                    a,b,c = res[i],res[j],res[k]
                    flag = 1
                    break
                elif(x < num):
                    j += 1
                else:
                    k -= 1
            if(flag == 1):
                break
            i += 1
        if(a == -1):
            print('NO')
        else:
            print('YES')
            print(a,b,c)