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 pm(n):
    arr = []
    while(n%2==0):
        arr.append(2)
        n//=2
    for  i in range(3,int(pow(n,0.5))+1,2):
        while n%i==0:
            arr.append(i)
            n//=i
    if n>2:
        arr.append(n)
    return arr

tc = int(input())
for ii in range(tc):
    n = int(input())
    arr = pm(n)
    a = arr[0]
    b = 1
    c = 1
    index = 0
    for i in range(1,len(arr)):
        b*=arr[i]
        if b!=a:
            index = i
            break
    for j in range(index+1,len(arr)):
        c*=arr[j]


    if a!=b and b!=c and a!=c and a!=1 and b!=1 and c!=1:
        print("YES")
        print(a,b,c)
    else:
        print("NO")