Problem: You are given an integer N.

Find a triple of positive integers h, n and w such that 4/N = 1/h + 1/n + 1/w.

If there are multiple solutions, any of them will be accepted.

Constraints

* It is guaranteed that, for the given integer N, there exists a solution such that h,n,w \leq 3500.

Inputs

Input is given from Standard Input in the following format:


N


Outputs

Print a triple of positive integers h, n and w that satisfies the condition, in the following format:


h n w

Examples

Input

2


Output

1 2 2


Input

3485


Output

872 1012974 1539173474040


Input

4664


Output

3498 3498 3498

Solution (in PYTHON):

Solution:
import math

originN = int(raw_input())
N = originN
primes = []
while True:
    if N % 2 == 0:
        primes.append(2)
        N /= 2
    else:
        break
i = 3
while True:
    if N == 1 or N < i**2:
        break
    while True:
        if N % i == 0:
            primes.append(i)
            N /= i
        else:
            break
    i += 2
if N != 1:
    primes.append(N)
if primes[0] == 2:
    print str(originN/2)+" "+str(originN)+" "+str(originN)
elif primes[0] == 3:
    print str(originN/3)+" "+str(originN*2)+" "+str(originN*2)
else:
    p = int(math.ceil(float(primes[0])/4.0))
    if primes[0] % 4 == 1:
        if p % 2 == 0:
            print str(originN/primes[0]*p)+" "+str(originN*p/2)+" "+str(originN*p)
        else:
            isValid = False
            for h in xrange(1, 3501):
                for n in xrange(1, 3501):
                    if (4*n*h-n*originN-h*originN) > 0 and (originN*n*h) % (4*n*h-n*originN-h*originN) == 0:
                        isValid = True
                        print str(h)+" "+str(n)+" "+str((originN*n*h)/(4*n*h-n*originN-h*originN))
                        break
                if isValid: break
    else:
        print str(originN/primes[0]*p)+" "+str(originN*p*2)+" "+str(originN*p*2)