E. Game with Stonestime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputBob decided to take a break from calculus homework and designed a game for himself. The game is played on a sequence of piles of stones, which can be described with a sequence of integers s_1, \ldots, s_k, where s_i is the number of stones in the i-th pile. On each turn, Bob picks a pair of non-empty adjacent piles i and i+1 and takes one stone from each. If a pile becomes empty, its adjacent piles do not become adjacent. The game ends when Bob can't make turns anymore. Bob considers himself a winner if at the end all piles are empty.We consider a sequence of piles winning if Bob can start with it and win with some sequence of moves.You are given a sequence a_1, \ldots, a_n, count the number of subsegments of a that describe a winning sequence of piles. In other words find the number of segments [l, r] (1 \leq l \leq r \leq n), such that the sequence a_l, a_{l+1}, \ldots, a_r is winning.InputEach test consists of multiple test cases. The first line contains a single integer t (1 \leq t \leq 3 \cdot 10^5) — the number of test cases. Description of the test cases follows.The first line of each test case contains a single integer n (1 \leq n \leq 3 \cdot 10^5).The second line of each test case contains n integers a_1, a_2, \ldots, a_n (0 \leq a_i \leq 10^9).It is guaranteed that the sum of n over all test cases does not exceed 3 \cdot 10^5.OutputPrint a single integer for each test case — the answer to the problem.ExampleInput
6
2
2 2
3
1 2 3
4
1 1 1 1
4
1 2 2 1
4
1 2 1 2
8
1 2 1 2 1 2 1 2
Output
1
0
4
2
1
3
NoteIn the first test case, Bob can't win on subsegments of length 1, as there is no pair of adjacent piles in an array of length 1.In the second test case, every subsegment is not winning.In the fourth test case, the subsegment [1, 4] is winning, because Bob can make moves with pairs of adjacent piles: (2, 3), (1, 2), (3, 4). Another winning subsegment is [2, 3].
6
2
2 2
3
1 2 3
4
1 1 1 1
4
1 2 2 1
4
1 2 1 2
8
1 2 1 2 1 2 1 2

1 0 4 2 1 3 
['binary search', 'data structures', 'games', 'greedy', '*2300']