Subarrays with sum K

Count the contiguous subarrays whose elements add up to exactly K.

Reported in: HCLTech (memory-based)

Input

First line: N. Second line: N integers (may be negative). Third line: K.

Output

The number of subarrays.

Constraints

1 ≤ N ≤ 10^5.

Example 1

Input:
5
1 2 3 -2 2
3

Output:
4

Example 2

Input:
3
1 1 1
2

Output:
2

Hint: Use prefix sums and a dictionary counting how often each prefix sum has appeared.

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