Description

You're given a polynomial, the coefficients of which are all integers. Now, it's your time to find out all the integral roots of it! Just try your best!

Input

The input consists of several test cases.
The first line of each test case contains an integer N ( N ≤ 100).
The second line of each test case contains N integers, a_n-1, ..., a₀, these numbers represents the polynomial: xⁿ + a_n-1 × x^n-1 ... + a₀. ( All a_i fits in 32-bit signed integer)

Output

Output the answers for each test case. The first line contains an integer R, the number of integral roots of the given polynomial. Each of the next R lines contains a root of the given polynomial. They should be outputed in non-descending order. Note if the polynomial has multiple roots you must output all of them.

4
1 0 -1 -1
2
2 1

2
-1
1 
2
-1
-1

Source

, Zhou Dong