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Count Pairs With Xor In A Range

Given an integer array nums and two integers low and high. Count number of pairs of indexes (i, j) for which both of this expression's are satisfied: 1. 0 <= i < j < nums.length 2. low <= nums[i] ^ nums[j] <= high

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Count Pairs With Xor In A Range

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Given an integer array nums and two integers low and high. Count number of pairs of indexes (i, j) for which both of this expression's are satisfied: 1. 0

Constraints

1. 1 <= nums.length <= 2 * 10^4 2. 1 <= nums[i] <= 2 * 10^4 3. 1 <= low <= high <= 2 * 10^4

Format

Input

Input is managed for you

Output

Output is managed for you

Example

Sample Input

4 1 4 2 7 3 5

Sample Output

4

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