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We define f (X, Y) as number of different corresponding bits in binary representation of X and Y. For example, f (2, 7) = 2, since binary representation of 2 and 7 are 010 and 111, respectively. The first and the third bit differ, so f (2, 7) = 2.

You are given an array **A** of **N** integers, A_{1}, A_{2} ,…, A_{N}. Find sum of f(A_{i}, A_{j}) for all pairs (i, j) such that 1 ≤ i, j ≤ N. Return the answer modulo 10^{9}+7.

**Example 1:**

**Input:** N = 2
A = {2, 4}
**Output:** 4
**Explaintion:** We return
f(2, 2) + f(2, 4) +
f(4, 2) + f(4, 4) =
0 + 2 +
2 + 0 = 4.

**Example 2:**

**Input:** N = 3
A = {1, 3, 5}
**Output:** 8
**Explaination:** We return
f(1, 1) + f(1, 3) + f(1, 5) +
f(3, 1) + f(3, 3) + f(3, 5) +
f(5, 1) + f(5, 3) + f(5, 5) =
0 + 1 + 1 +
1 + 0 + 2 +
1 + 2 + 0 = 8.

**Your Task:**

You do not need to read input or print anything. Your task is to complete the function **countBits()** which takes the value N and the array A as input parameters and returns the desired count modulo 10^{9}+7.

**Expected Time Complexity:** O(N)

**Expected Auxiliary Space:** O(1)

**Constraints:**

1 ≤ N ≤ 10^{4}

-2,147,483,648 ≤ A[i] ≤ 2,147,483,647

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Bit Difference

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