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

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