Bob and Alice are playing with an array $A[]$ of $n$ elements with Bob starting the game. In each turn:

1. A player picks a non-zero number of elements from $A[]$ with the same value and remove it from $A[]$.
2. The player whose turn makes array $A[]$ empty wins the game.

Alice modifies the game a bit. She selects some distinct elements that are present in $A[]$ and removes all other elements that are not selected from $A[]$. Now, the game is played using this modified array. For example, if $A = [1,1,3,12,2,34,2]$ and Alice selects values $(1,\ 2,\ 34)$, then the array with which the game is played is $[1,\ 1,\ 2,\ 34,\ 2]$.

Find the number of possible subsets of elements that Alice can select to modify $A[]$ such that Alice must win if both the players play optimally.

Note 

• Consider an empty subset as a valid answer.
• Since the number of possible subsets can be large, print the answer modulo $10^9 + 7$.

Input format

• The first line contains $N$.
• The next line contains $N$ space-separated integers denoting the elements of $A[]$.

Output format

Print the number of possible subsets of elements that Alice can select to modify $A[]$ such that Alice must win if both the players play optimally modulo $10^9 + 7$.

Constraints
$1 \le N \le 100000\\ 1 \le A[i] \le 100$