Given an array \(A\) of \(N \) integers. Find the number of unordered pairs \((i,j)\), \(1 \leq i, j \leq N\) such that 

• \(L \le A[i] + A[j] \le R\)
• \(A[i] \oplus A[j]\) is odd where \(\oplus\) represents bitwise XOR operation.

Input format

• The first line contains three space-separated integers \(N \ L \ R\).
• The next line contains \(N\) space-separated integers denoting the array \(A\)

Output format

Print the number of unordered pairs \((i,j)\) which satisfy the above conditions in a new line.

Constraints

\(1 \le N \le 10^5 \\ 1 \le L \le R \le 10^{18} \\ 1 \le A[i] \le 10^{18} \)