D - Xor Sum 2

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

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

xorの説明

• xor の値を X とおく。X2 進数表記したときの 2^k ( 0 \leq k, k は整数 ) の位の値は、c_1, c_2, ...c_m のうち、2 進数表記したときの 2^k の位の値が 1 となるものが奇数個ならば 1、偶数個ならば 0 となる。

### 制約

• 1 \leq N \leq 2 \times 10^5
• 0 \leq A_i < 2^{20}
• 入力はすべて整数である

### 入力

N
A_1 A_2 ... A_N


### 入力例 1

4
2 5 4 6


### 出力例 1

5


### 入力例 2

9
0 0 0 0 0 0 0 0 0


### 出力例 2

45


### 入力例 3

19
885 8 1 128 83 32 256 206 639 16 4 128 689 32 8 64 885 969 1


### 出力例 3

37


Score : 500 points

### 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.

Definition of XOR

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.

### Constraints

• 1 \leq N \leq 2 \times 10^5
• 0 \leq A_i < 2^{20}
• All values in input are integers.

### Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N


### Output

Print the number of the pairs of integers l and r (1 \leq l \leq r \leq N) that satisfy the condition.

### Sample Input 1

4
2 5 4 6


### Sample Output 1

5


(l,r)=(1,1),(2,2),(3,3),(4,4) clearly satisfy the condition. (l,r)=(1,2) also satisfies the condition, since A_1\ xor\ A_2 = A_1\ +\ A_2 = 7. There are no other pairs that satisfy the condition, so the answer is 5.

### Sample Input 2

9
0 0 0 0 0 0 0 0 0


### Sample Output 2

45


### Sample Input 3

19
885 8 1 128 83 32 256 206 639 16 4 128 689 32 8 64 885 969 1


### Sample Output 3

37