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After a trip with Sakurako, Kousuke was very scared because he forgot about his programming assignment. In this assignment, the teacher gave him an array $$$a$$$ of $$$n$$$ integers and asked him to calculate the number of non-overlapping segments of the array $$$a$$$, such that each segment is considered beautiful.

A segment $$$[l,r]$$$ is considered beautiful if $$$a_l + a_{l+1} + \dots + a_{r-1} + a_r=0$$$.

For a fixed array $$$a$$$, your task is to compute the maximum number of non-overlapping beautiful segments.

Input

The first line of input contains the number $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. Each test case consists of $$$2$$$ lines.

The first line contains one integer $$$n$$$ ($$$1 \le n \le 10^5$$$) — the length of the array.
The second line contai

Kousuke's Assignment

Examples