In this problem you are given six simple equations. You are also informed that correct values of x1, x2, x3, x5, x6, x7, are in the answer set A = {a1, a2, a3,…,an} for some integer n, where each ai is in the set of prime numbers between 2 to 20,000,000. The six equations are as follows.

c₁ = x₁x₂

x₄ = c₄x₁

c₃ = x₆x₇

x₈ = x₇c₂

c₅ = x₂x₃

c₆ = x₆x₅

   Observe that c1, c2, c3, c4, c5, and c6 are positive integer constants at most (20,000,000)2. Given c1, c2, c3, c4, c5, and c6, your job is to find an efficient algorithm to solve these equations and report the correct values of x1, x2, x3, x5, x6, x7. You can be sure that these equations can be solved.

Input

   The input file contains 6 integers separated by a blank representing c1, c2, c3, c4, c5, and c6, respectively.

Output

   The output file has a single line reporting the correct values of x1, x2, x3, x5, x6, x7, respectively. Each value is separated by a blank. (In case there are many possible solutions, choose only one of them as the output.)

Examples