CF1748C.Zero-Sum Prefixes

The score of an array $v_1,v_2,\ldots,v_n$ is defined as the number of indices $i$ ( $1 \le i \le n$ ) such that $v_1+v_2+\ldots+v_i = 0$ .

You are given an array $a_1,a_2,\ldots,a_n$ of length $n$ . You can perform the following operation multiple times:

• select an index $i$ ( $1 \le i \le n$ ) such that $a_i=0$ ;
• then replace $a_i$ by an arbitrary integer.

What is the maximum possible score of $a$ that can be obtained by performing a sequence of such operations?

Each test contains multiple test cases. The first line contains a single integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases.

The first line of each test case contains one integer $n$ ( $1 \le n \le 2 \cdot 10^5$ ) — the length of the array $a$ .

The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ( $-10^9 \le a_i \le 10^9$ ) — array $a$ .

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ .

For each test case, print the maximum possible score of the array $a$ after performing a sequence of operations.

In the first test case, it is optimal to change the value of $a_2$ to $-2$ in one operation.

The resulting array $a$ will be $[2,-2,1,-1,0]$ , with a score of $3$ :

• $a_1+a_2=2-2=0$ ;
• $a_1+a_2+a_3+a_4=2-2+1-1=0$ ;
• $a_1+a_2+a_3+a_4+a_5=2-2+1-1+0=0$ .

In the second test case, it is optimal to change the value of $a_3$ to $-2\,000\,000\,000$ , giving us an array with a score of $1$ .

In the third test case, it is not necessary to perform any operations.