Problem Statement

There is an integer sequence A of length N.

Find the number of the pairs of integers l and r (1 \leq l \leq r \leq N) that satisfy the following condition:

• A_l\ xor\ A_{l+1}\ xor\ ...\ xor\ A_r = A_l\ +\ A_{l+1}\ +\ ...\ +\ A_r

Here, xor denotes the bitwise exclusive OR.

The XOR of integers c_1, c_2, ..., c_m is defined as follows:

• Let the XOR be X. In the binary representation of X, the digit in the 2^k's place (0 \leq k; k is an integer) is 1 if there are an odd number of integers among c_1, c_2, ...c_m whose binary representation has 1 in the 2^k's place, and 0 if that number is even.

For example, let us compute the XOR of 3 and 5. The binary representation of 3 is 011, and the binary representation of 5 is 101, thus the XOR has the binary representation 110, that is, the XOR is 6.