Your task is to count the number of ways numbers 1,2,\ldots,n can be divided into two sets of equal sum.

For example, if n=7, there are four solutions:

• \{1,3,4,6\} and \{2,5,7\}
• \{1,2,5,6\} and \{3,4,7\}
• \{1,2,4,7\} and \{3,5,6\}
• \{1,6,7\} and \{2,3,4,5\}

Input

The only input line contains an integer n.

Output

Print the answer modulo 10^9+7.

Constraints

• 1 \le n \le 500

Example

Input:

7

Output:

4