Sending a Sequence Over the Network

题意翻译

你现在有一个序列 $a$，定义一个用该序列生成新序列 $b$ 的规则如下： + 把 $a$ 这个序列分成**连续**的几段； + 对于每一段，我们把这一段的长度插入到**这一段**的左边**或**右边。 + 每一段进行操作后便得到了 $b$ 序列。 比如 $a$ = $[1,2,3,1,2,3]$ ，我们可以把其分成 $\color {red}[1]$，$\color {blue}[2,3,1]$，$\color {green}[2,3]$，长度分别为 $1$，$3$，$2$。 然后我们把长度随意插入原序列中，可以得到一个不唯一的 $b$ 序列，例如：$b = [\color {black}{1,}\color {red}1\color {black},3,\color {blue}{2,3,1},\color {black}2,\color {green}{3,2}]$。 现在给定一个长度为 $n$ $(1≤n≤2 \times 10^5)$ 已经操作后的序列 $b$ $(1\le b_i \le 10^9)$，询问你是否能构造出任意一个原序列 $a$，使得它进行如上操作后可以得到 $b$，若能构造出输出 `YES`，否则输出 `NO`。 共有 $t$ $(1 \le t \le 10^4)$ 组数据，$\sum n \le 2 \times 10^5$。 **请注意常数可能造成的影响，否则可能会出现 TLE 等评测结果。**

题目描述

The sequence $ a $ is sent over the network as follows: 1. sequence $ a $ is split into segments (each element of the sequence belongs to exactly one segment, each segment is a group of consecutive elements of sequence); 2. for each segment, its length is written next to it, either to the left of it or to the right of it; 3. the resulting sequence $ b $ is sent over the network. For example, we needed to send the sequence $ a = [1, 2, 3, 1, 2, 3] $ . Suppose it was split into segments as follows: $ [\color{red}{1}] + [\color{blue}{2, 3, 1}] + [\color{green}{2, 3}] $ . Then we could have the following sequences: - $ b = [1, \color{red}{1}, 3, \color{blue}{2, 3, 1}, \color{green}{2, 3}, 2] $ , - $ b = [\color{red}{1}, 1, 3, \color{blue}{2, 3, 1}, 2, \color{green}{2, 3}] $ , - $ b = [\color{red}{1}, 1, \color{blue}{2, 3, 1}, 3, 2, \color{green}{2, 3}] $ , - $ b = [\color{red}{1}, 1,\color{blue}{2, 3, 1}, 3, \color{green}{2, 3}, 2] $ . If a different segmentation had been used, the sent sequence might have been different. The sequence $ b $ is given. Could the sequence $ b $ be sent over the network? In other words, is there such a sequence $ a $ that converting $ a $ to send it over the network could result in a sequence $ b $ ?

输入输出格式

输入格式

The first line of input data contains a single integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. Each test case consists of two lines. The first line of the test case contains an integer $ n $ ( $ 1 \le n \le 2 \cdot 10^5 $ ) — the size of the sequence $ b $ . The second line of test case contains $ n $ integers $ b_1, b_2, \dots, b_n $ ( $ 1 \le b_i \le 10^9 $ ) — the sequence $ b $ itself. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

输出格式

For each test case print on a separate line: - YES if sequence $ b $ could be sent over the network, that is, if sequence $ b $ could be obtained from some sequence $ a $ to send $ a $ over the network. - NO otherwise. You can output YES and NO in any case (for example, strings yEs, yes, Yes and YES will be recognized as positive response).

输入输出样例

输入样例 #1

7
9
1 1 2 3 1 3 2 2 3
5
12 1 2 7 5
6
5 7 8 9 10 3
4
4 8 6 2
2
3 1
10
4 6 2 1 9 4 9 3 4 2
1
1

输出样例 #1

YES
YES
YES
NO
YES
YES
NO

说明

In the first case, the sequence $ b $ could be obtained from the sequence $ a = [1, 2, 3, 1, 2, 3] $ with the following partition: $ [\color{red}{1}] + [\color{blue}{2, 3, 1}] + [\color{green}{2, 3}] $ . The sequence $ b $ : $ [\color{red}{1}, 1, \color{blue}{2, 3, 1}, 3, 2, \color{green}{2, 3}] $ . In the second case, the sequence $ b $ could be obtained from the sequence $ a = [12, 7, 5] $ with the following partition: $ [\color{red}{12}] + [\color{green}{7, 5}] $ . The sequence $ b $ : $ [\color{red}{12}, 1, 2, \color{green}{7, 5}] $ . In the third case, the sequence $ b $ could be obtained from the sequence $ a = [7, 8, 9, 10, 3] $ with the following partition: $ [\color{red}{7, 8, 9, 10, 3}] $ . The sequence $ b $ : $ [5, \color{red}{7, 8, 9, 10, 3}] $ . In the fourth case, there is no sequence $ a $ such that changing $ a $ for transmission over the network could produce a sequence $ b $ .

题意翻译

你现在有一个序列 $a$，定义一个用该序列生成新序列 $b$ 的规则如下： + 把 $a$ 这个序列分成**连续**的几段； + 对于每一段，我们把这一段的长度插入到**这一段**的左边**或**右边。 + 每一段进行操作后便得到了 $b$ 序列。 比如 $a$ = $[1,2,3,1,2,3]$ ，我们可以把其分成 $\color {red}[1]$，$\color {blue}[2,3,1]$，$\color {green}[2,3]$，长度分别为 $1$，$3$，$2$。 然后我们把长度随意插入原序列中，可以得到一个不唯一的 $b$ 序列，例如：$b = [\color {black}{1,}\color {red}1\color {black},3,\color {blue}{2,3,1},\color {black}2,\color {green}{3,2}]$。 现在给定一个长度为 $n$ $(1≤n≤2 \times 10^5)$ 已经操作后的序列 $b$ $(1\le b_i \le 10^9)$，询问你是否能构造出任意一个原序列 $a$，使得它进行如上操作后可以得到 $b$，若能构造出输出 `YES`，否则输出 `NO`。 共有 $t$ $(1 \le t \le 10^4)$ 组数据，$\sum n \le 2 \times 10^5$。 **请注意常数可能造成的影响，否则可能会出现 TLE 等评测结果。**