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.