CF1584E.Game with Stones

Bob 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.

鲍勃决定暂时放下微积分作业，为自己设计了一个游戏。

该游戏在一个石堆序列上进行，该序列可用一串整数 $s_1, \ldots, s_k$ 描述，其中 $s_i$ 表示第 $i$ 个石堆中的石子数量。在每一轮中，鲍勃选择一对非空且相邻的石堆 $i$ 和 $i+1$，并从每个石堆中各取走一颗石子。若某个石堆变为空，则其相邻石堆不会因此变为相邻。当鲍勃无法再进行任何操作时，游戏结束。若游戏结束时所有石堆均为空，鲍勃便认为自己获胜。

我们称一个石堆序列为“获胜序列”，如果鲍勃可以从该序列出发，并通过某种操作序列赢得游戏。

现给定一个序列 $a_1, \ldots, a_n$，请计算该序列中有多少个子段（连续子数组）描述了一个获胜序列。换言之，求满足条件的区间 $[l, r]$（其中 $1 \leq l \leq r \leq n$）的个数，使得子序列 $a_l, a_{l+1}, \ldots, a_r$ 是一个获胜序列。

Each 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 $3 \cdot 10^5$.

每个测试包含多个测试用例。第一行包含一个整数 $t$（$1 \leq t \leq 3 \cdot 10^5$），表示测试用例的数量。随后是各测试用例的描述。

每个测试用例的第一行包含一个整数 $n$（$1 \leq n \leq 3 \cdot 10^5$）。

每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$0 \leq a_i \leq 10^9$）。

保证所有测试用例的 $n$ 值之和不超过 $3 \cdot 10^5$。

Print a single integer for each test case — the answer to the problem.

对每个测试用例，输出一个整数——即该问题的答案。

In 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 $[2, 3]$.

在第一个测试用例中，Bob 无法在长度为 $1$ 的子段上获胜，因为长度为 $1$ 的数组中不存在相邻的两堆石子。

在第二个测试用例中，所有子段均非获胜子段。

在第四个测试用例中，子段 $[1, 4]$ 是获胜子段，因为 Bob 可以对相邻石子堆进行如下操作：$(2, 3)$、$(1, 2)$、$(3, 4)$。另一个获胜子段是 $[2, 3]$。