Mathematician Number

Problem Statement

\ \ Mathematician\\\'s Number \ UNSOLVED \ \ \ \ A Mathematician has N numbers on his board. He hates numbers so much that he wants only one number to remain on the board, so he devises a special tactic to do so. \ \ He randomly picks 2 numbers, say A and B. He erase both of them and add a new number equals to: \ \ A - B if (both are even or both are odd) \ A + B if (one is even and other is odd) \ \ \ After each move 1 number is reduced from the board. After a certain number of operations there would be only one number remaining on the board. \ \ The Mathematician wants to know how many different final numbers can be produced. \ \ \ \ Input Format \ \ The first line contains N, the number of integers initially present in the board. \ The second line contains N space separated integers A1, A2, A3... AN, denoting the numbers in the board. \ \ \ \ \ Output Format \ A single output representing the count denoting the number of possible final distinct numbers on the board. \ \ \ \ Constrai