Array Sharpening

题意翻译

- 定义一个序列 $a_1,a_2,\cdots,a_n$ 是“整齐的”当且仅当存在一个 $1\le k\le n$ 使得 $a_1<a_2<\cdots<a_k>a_{k+1}>a_{k+2}>\cdots$，或者说存在一个分界线使左半边**严格**单调递增而右半边**严格**单调递减。 - 给定一个非负整数序列 $a_1,a_2,\cdots,a_n$，每次可以使其中一个正整数的值 $-1$，问能否把它变成整齐的。 - 多组数据，所有数据的 $n$ 之和不超过 $3\times10^5$。

题目描述

You're given an array $ a_1, \ldots, a_n $ of $ n $ non-negative integers. Let's call it sharpened if and only if there exists an integer $ 1 \le k \le n $ such that $ a_1 < a_2 < \ldots < a_k $ and $ a_k > a_{k+1} > \ldots > a_n $ . In particular, any strictly increasing or strictly decreasing array is sharpened. For example: - The arrays $ [4] $ , $ [0, 1] $ , $ [12, 10, 8] $ and $ [3, 11, 15, 9, 7, 4] $ are sharpened; - The arrays $ [2, 8, 2, 8, 6, 5] $ , $ [0, 1, 1, 0] $ and $ [2, 5, 6, 9, 8, 8] $ are not sharpened. You can do the following operation as many times as you want: choose any strictly positive element of the array, and decrease it by one. Formally, you can choose any $ i $ ( $ 1 \le i \le n $ ) such that $ a_i>0 $ and assign $ a_i := a_i - 1 $ . Tell if it's possible to make the given array sharpened using some number (possibly zero) of these operations.

输入输出格式

输入格式

The input consists of multiple test cases. The first line contains a single integer $ t $ ( $ 1 \le t \le 15\ 000 $ ) — the number of test cases. The description of the test cases follows. The first line of each test case contains a single integer $ n $ ( $ 1 \le n \le 3 \cdot 10^5 $ ). The second line of each test case contains a sequence of $ n $ non-negative integers $ a_1, \ldots, a_n $ ( $ 0 \le a_i \le 10^9 $ ). It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 3 \cdot 10^5 $ .

输出格式

For each test case, output a single line containing "Yes" (without quotes) if it's possible to make the given array sharpened using the described operations, or "No" (without quotes) otherwise.

输入输出样例

输入样例 #1

10
1
248618
3
12 10 8
6
100 11 15 9 7 8
4
0 1 1 0
2
0 0
2
0 1
2
1 0
2
1 1
3
0 1 0
3
1 0 1

输出样例 #1

Yes
Yes
Yes
No
No
Yes
Yes
Yes
Yes
No

说明

In the first and the second test case of the first test, the given array is already sharpened. In the third test case of the first test, we can transform the array into $ [3, 11, 15, 9, 7, 4] $ (decrease the first element $ 97 $ times and decrease the last element $ 4 $ times). It is sharpened because $ 3 < 11 < 15 $ and $ 15 > 9 > 7 > 4 $ . In the fourth test case of the first test, it's impossible to make the given array sharpened.

题意翻译

- 定义一个序列 $a_1,a_2,\cdots,a_n$ 是“整齐的”当且仅当存在一个 $1\le k\le n$ 使得 $a_1<a_2<\cdots<a_k>a_{k+1}>a_{k+2}>\cdots$，或者说存在一个分界线使左半边**严格**单调递增而右半边**严格**单调递减。 - 给定一个非负整数序列 $a_1,a_2,\cdots,a_n$，每次可以使其中一个正整数的值 $-1$，问能否把它变成整齐的。 - 多组数据，所有数据的 $n$ 之和不超过 $3\times10^5$。