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First Move In A Nim Game

Two players Alice and Bob are playing NIM Game with each other. Both are playing optimally.Alice starts the game. The task is to find the number of ways of playing 1st move for Alice to ensure a winning strategy for him if possible, otherwise print -1.

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First Move In A Nim Game

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Two players Alice and Bob are playing NIM Game with each other. Both are playing optimally.Alice starts the game. The task is to find the number of ways of playing 1st move for Alice to ensure a winning strategy for him if possible, otherwise print -1.

Constraints

1<= n <= 10^5 1<= A[i] <= 10^8

Format

Input

The first line contains one integer n. The second line contains n space separated integers a[1],a[2]...a[n].

Output

Print the number of possible first move for Alice to win. If Alice can't win, Print -1.

Example

Sample Input

7 24 6 10 56 9 1 24

Sample Output

1

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