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:
#!/usr/bin/env python
import os
import sys
from io import BytesIO, IOBase
#from bisect import bisect_left as bl                #c++ lowerbound bl(array,element)
#from bisect import bisect_right as br               #c++ upperbound br(array,element)
 
from collections import defaultdict 
import math
def main():
    for _ in range(int(input())):
        n=int(input())
        data=defaultdict(lambda:0)
        for x in range(2,math.floor(math.sqrt(n))+1):
            if n%x==0:
                while n%x==0:
                    n=n//x
                    data[x]=data[x]+1
        if n!=1:
            data[n]+=1
        ele=[]
        #print(data)
        if len(data.keys())>=3:
            for x,y in data.items():
                if len(ele)==3:
                    ele[2]*=(x**y)
                else:
                    ele.append(x**y)
            print("YES")
            print(*ele)
        elif len(data.keys())==2:
            dat=sorted(data.items(),key=lambda x:x[0])
            if dat[0][1]>=3:
                ele.append(dat[0][0])
                ele.append(dat[0][0]**(dat[0][1]-1))
                ele.append(dat[1][0]**(dat[1][1]))
                print("YES")
                print(*ele)
            elif dat[1][1]>=3:
                ele.append(dat[1][0])
                ele.append(dat[1][0]**(dat[1][1]-1))
                ele.append(dat[0][0]**(dat[0][1]))
                print("YES")
                print(*ele)
            elif dat[0][1]>=2 and dat[1][1]>=2:
                ele.append(dat[0][0])
                ele.append(dat[1][0])
                ele.append(dat[1][0]**(dat[1][1]-1)*dat[0][0]**(dat[0][1]-1))
                print("YES")
                print(*ele)
            else:
                print("NO")
        elif len(data.keys())==1:
            done=False
            for x,y in data.items():
                if y>=6:
                    print("YES")
                    print(x,x**2,x**(y-3))
                else:
                    print("NO")
        else:
            print("NO")
        
        




                

                






#-----------------------------BOSS-------------------------------------!
# region fastio

BUFSIZE = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")

# endregion

if __name__ == "__main__":
    main()