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.
#!/usr/bin/env python
"""
This file is part of https://github.com/Cheran-Senthil/PyRival.
Copyright 2019 Cheran Senthilkumar <hello@cheran.io>

"""
from __future__ import division, print_function

import cmath
import itertools
import math
import operator as op
import random
import sys
from atexit import register
from bisect import bisect_left, bisect_right
from collections import Counter
# from copy import deepcopy
# from decimal import Decimal
# from difflib import SequenceMatcher
from functools import reduce
# from heapq import heappop, heappush
from io import BytesIO, FileIO, StringIO


if sys.version_info[0] < 3:
    class dict(dict):
        """dict() -> new empty dictionary"""
        def items(self):
            """D.items() -> a set-like object providing a view on D's items"""
            return dict.iteritems(self)

        def keys(self):
            """D.keys() -> a set-like object providing a view on D's keys"""
            return dict.iterkeys(self)

        def values(self):
            """D.values() -> an object providing a view on D's values"""
            return dict.itervalues(self)

    input = raw_input
    range = xrange

    filter = itertools.ifilter
    map = itertools.imap
    zip = itertools.izip


def gcd(x, y):
    """greatest common divisor of x and y"""
    while y:
        x, y = y, x % y
    return x


INP_FILE = 0
OUT_FILE = 1

if sys.version_info[0] < 3:
    sys.stdin = BytesIO(FileIO(INP_FILE).read())
    sys.stdout = BytesIO()
    register(lambda: FileIO(OUT_FILE, 'w').write(sys.stdout.getvalue()))
else:
    sys.stdin = StringIO(FileIO(INP_FILE).read().decode())
    sys.stdout = StringIO()
    register(lambda: FileIO(OUT_FILE, 'w').write(sys.stdout.getvalue().encode()))

input = lambda: sys.stdin.readline().rstrip('\r\n')


def memodict(f):
    """ Memoization decorator for a function taking a single argument. """
    class memodict(dict):
        def __missing__(self, key):
            ret = self[key] = f(key)
            return ret
    return memodict().__getitem__


def is_prime(n):
    """
    Deterministic variant of the Miller-Rabin primality test to determine
    whether a given number (upto 2**64) is prime.

    Parameters
    ----------
    n : int
        n >= 0, an integer to be tested for primality.

    Returns
    -------
    bool
        False if n is composite, otherwise True.
    """
    if n in [2, 3, 5, 13, 19, 73, 193, 407521, 299210837]:
        return True

    if (n in [0, 1]) or (any((n % p) == 0 for p in [2, 3, 5, 13, 19, 73, 193, 407521, 299210837])):
        return False

    d, s = n - 1, 0
    while not d % 2:
        d, s = d >> 1, s + 1

    def try_composite(a):
        if pow(a, d, n) == 1:
            return False
        for i in range(s):
            if pow(a, 2**i * d, n) == n - 1:
                return False
        return True

    return not any(try_composite(w) for w in [2, 325, 9375, 28178, 450775, 9780504, 1795265022])


@memodict
def pollard_rho(n):
    if n == 1:
        return Counter()

    if is_prime(n):
        return Counter({n: 1})

    y, c, m = random.randint(1, n - 1), random.randint(1, n - 1), random.randint(1, n - 1)
    g, r, q = 1, 1, 1

    while g == 1:
        x, k = y, 0

        for _ in range(r):
            y = (y*y + c) % n

        while (k < r) and (g == 1):
            ys = y

            for _ in range(min(m, r - k)):
                y = (y*y + c) % n
                q = (q * abs(x - y)) % n

            g = gcd(q, n)
            k += m

        r *= 2

    if g == n:
        while True:
            ys = (ys*ys + c) % n
            g = gcd(abs(x - ys), n)
            if g > 1:
                break

    return pollard_rho(g) + pollard_rho(n // g)


def factors(n):
    """
    Prime factorization using Pollard's rho algorithm.

    Parameters
    ----------
    n : int
        n > 0, an integer to be factorized.

    Returns
    -------
    prime_factors : Counter
        Counter of the prime factors of n.
    """
    prime_factors = Counter()

    def ilog(n, p):
        cnt = 0
        while n % p == 0:
            n, cnt = n // p, cnt + 1
        return n, cnt

    if n % 2 == 0:
        n, prime_factors[2] = ilog(n, 2)
    if n % 3 == 0:
        n, prime_factors[3] = ilog(n, 3)

    i = 5
    while i * i <= min(n, 4294967295):
        if n % i == 0:
            n, prime_factors[i] = ilog(n, i)
        i += 2 if i % 3 == 2 else 4

    if n == 1:
        return prime_factors

    if n <= 4294967295:
        prime_factors[n] = 1
        return prime_factors

    return prime_factors + pollard_rho(n)


def main():
    n = int(input())

    f = factors(n)
    p = list(f.values())

    a2 = (max(p) - 1).bit_length()
    print(reduce(op.mul, f.keys()), (len(set(p)) != {1 << a2}) + a2)


if __name__ == '__main__':
    main()
