Prime Factorization

Factorize a given integer n.

Input

n

An integer n is given in a line.

Output

Print the given integer n and :. Then, print prime factors in ascending order. If n is divisible by a prime factor several times, the prime factor should be printed according to the number of times. Print a space before each prime factor.

Constraints

• 2 ≤ n ≤ 10⁹

Sample Input 1

12

Sample Output 1

12: 2 2 3

Sample Input 2

126

Sample Output 2

126: 2 3 3 7

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