You are given an integer array A of size N.

The stability score is defined as:

• The number of indices i such that after removing element A[i], 👉 Sum of elements at even indices = Sum of elements at odd indices

Important points:

• After removing an element, the array re-indexes (shifts left)

• So indices change — this is critical

Your task:

• Return the total count of such indices

📥 Input Format

• First line: Integer array A

📤 Output Format

• A single integer → stability score

⚙️ Constraints

• 1≤N≤1051 \le N \le 10^51≤N≤105

• 1≤A[i]≤1041 \le A[i] \le 10^41≤A[i]≤104

🧪 Examples

Input:

2 1 6 4

Output:

1

Explanation: Remove index 1 → [2,6,4]

• Even sum = 2 + 4 = 6

• Odd sum = 6 ✔ Balanced → count = 1