Count them!
"The Hindus came up with a good religion" V.S. Vysotsky
We are all familiar with the classic game of Nim. In this game, there are several piles of stones, and players take turns. During each turn, a player can remove any number of stones from a single pile. The player who cannot make a move loses the game.
In this scenario, Buddhists Lao Czdong and Confucius Czdong are playing this intriguing game. They are not concerned with who will win, as they view victory as merely a source of vanity. Instead, they are more interested in determining how many winning moves the first player has. However, Lao and Confucius do not wish to count these winning moves themselves, so they have asked for your help in finding this number.
Input
The first line of the input contains a single natural number N ≤ 10^5, which represents the number of Nim piles. The second line lists the sizes of these piles, separated by spaces. Each pile can have a size of up to 10^9.
Output
Your task is to output the number of winning moves available to the first player.