JATC's math teacher always gives the class some interesting math problems so that they don't get bored. Today the problem is as follows. Given an integer n, you can perform the following operations zero or more times:

  * mul x: multiplies n by x (where x is an arbitrary positive integer). 
  * sqrt: replaces n with √{n} (to apply this operation, √{n} must be an integer). 



You can perform these operations as many times as you like. What is the minimum value of n, that can be achieved and what is the minimum number of operations, to achieve that minimum value?

Apparently, no one in the class knows the answer to this problem, maybe you can help them?

Input

The only line of the input contains a single integer n (1 ≤ n ≤ 10^6) — the initial number.

Output

Print two integers: the minimum integer n that can be achieved using the described operations and the minimum number of operations required.

Examples

Input

20


Output

10 2

Input

5184


Output

6 4

Note

In the first example, you can apply the operation mul 5 to get 100 and then sqrt to get 10.

In the second example, you can first apply sqrt to get 72, then mul 18 to get 1296 and finally two more sqrt and you get 6.

Note, that even if the initial value of n is less or equal 10^6, it can still become greater than 10^6 after applying one or more operations.
from __future__ import division, print_function
 
import os,sys
from io import BytesIO, IOBase
 
if sys.version_info[0] < 3:
    from __builtin__ import xrange as range
    from future_builtins import ascii, filter, hex, map, oct, zip
from itertools import permutations 
 
def ii():  return int(input())
def si():  return input()
def mi():  return map(int,input().split(" "))
def msi(): return map(str,input().split(" "))
def li():  return list(mi())
 
def dmain():
    sys.setrecursionlimit(1000000)
    threading.stack_size(1024000)
    thread = threading.Thread(target=main)
    thread.start()
    
import math
def getSum(n): 
    sum = 0
    while(n > 0): 
        sum += int(n%10) 
        n = int(n/10) 
  
    return sum

def isPowerOfTwo (x): return (x and (not(x & (x - 1))) )
 
def gcd(x, y):
    while y:
        x, y = y, x % y
    return x
def egcd(a, b):  
    if a == 0 :   
        return b, 0, 1
    gcd, x1, y1 = egcd(b%a, a)
    x = y1 - (b//a) * x1  
    y = x1  
     
    return gcd, x, y 
    
def checkPrime(n) : # Check Prime Number or not 
    if (n <= 1) : return False
    if (n <= 3) : return True
    if (n % 2 == 0 or n % 3 == 0) : return False
    i = 5
    while(i * i <= n) : 
        if (n % i == 0 or n % (i + 2) == 0) : 
            return False
        i = i + 6
    return True
def fib(n):
    if n==0:
        return (0,1)
    p=fib(n>>1)
    c=p[0]*(2*p[1]-p[0])
    d=p[0]*p[0]+p[1]*p[1]
    if (n&1):
        return c+2*d 
    else:
        return c+d 
def read():
    sys.stdin = open('input.txt', 'r')  
def powLog(x,y):
    res=1
    while y>0:
        if y&1:
            res=res*x
        x=x*x
        y>>=1
    return res

def primefactor(n): 
    d=dict()
    while n % 2 == 0: 
        if 2 in d:
            d[2]+=1
        else:
            d[2]=1 
        n = int(n / 2)
        
    for i in range(3,int(math.sqrt(n))+1,2): 
        while n % i== 0: 
            if i in d:
                d[i]+=1
            else:
                d[i]=1
            n = int(n / i)
            
    if n > 2: 
        if n in d:
            d[n]+=1
        else:
            d[n]=1
    return d
        


def main():
    n=ii()
    res=primefactor(n)
    print(math.prod(list(res.keys())))
# region fastio
# template taken from https://github.com/cheran-senthil/PyRival/blob/master/templates/template.py
 
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")
 
 
def print(*args, **kwargs):
    """Prints the values to a stream, or to sys.stdout by default."""
    sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout)
    at_start = True
    for x in args:
        if not at_start:
            file.write(sep)
        file.write(str(x))
        at_start = False
    file.write(kwargs.pop("end", "\n"))
    if kwargs.pop("flush", False):
        file.flush()
 
 
if sys.version_info[0] < 3:
    sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout)
else:
    sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
 
input = lambda: sys.stdin.readline().rstrip("\r\n")
 
# endregion
 
 
if __name__ == "__main__":
    #read()
    main()
    #dmain()
 
# Comment Read()