Given an array A[ ] of N integers and an integer X. In one operation, you can change the i^{th} element of the array to any integer value where 1 ≤ i ≤ N. Calculate minimum number of such operations required such that the bitwise AND of all the elements of the array is strictly greater than X.
Example 1:
Input:
N = 4, X = 2
A[] = {3, 1, 2, 7}
Output:
2
Explanation:
After performing two operations:
Modified array: {3, 3, 11, 7}
Now, Bitwise AND of all the elements
is 3 & 3 & 11 & 7 = 3
Example 2:
Input:
N = 3, X = 1
A[] = {2, 2, 2}
Output:
0
Your Task:
You don't need to read input or print anything. Your task is to complete the function count( ) which takes N, A[ ] and X as input parameters and returns the minimum number of operations required.
Expected Time Complexity: O(N * Log(max(A[ ])))
Expected Auxiliary Space: O(1)
Constraints:
1 ≤ N ≤ 10^{5}
1 ≤ A[i] ≤ 10^{9}
1 ≤ X ≤ 10^{9}

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