Nastya and Strange Generator

题意翻译

小D搞来了一个随机数生成器。 - 定义$r_j$表示$j$右边（包括$j$）第一个没有标记的位置。 - 定义$count_j$表示满足$r_i=j$的$i$的个数。 - 刚开始所有位置都没有被标记。 它的工作方法如下： 1. 找到当前$count$值最大且没有被标记的位置$i$。 2. 将输出序列的第$i$项设为已经被标记的位置的数量$+1$，并标记$i$的位置。 3. 如果还有数没有被标记，重复执行第一步。 现在给出你一个输出序列，问该输出序列可不可能是由上所说的随机数生成器生成的，如果有可能，输出`Yes`，否则输出`No`。

题目描述

Denis was very sad after Nastya rejected him. So he decided to walk through the gateways to have some fun. And luck smiled at him! When he entered the first courtyard, he met a strange man who was selling something. Denis bought a mysterious item and it was... Random permutation generator! Denis could not believed his luck. When he arrived home, he began to study how his generator works and learned the algorithm. The process of generating a permutation consists of $ n $ steps. At the $ i $ -th step, a place is chosen for the number $ i $ $ (1 \leq i \leq n) $ . The position for the number $ i $ is defined as follows: - For all $ j $ from $ 1 $ to $ n $ , we calculate $ r_j $ — the minimum index such that $ j \leq r_j \leq n $ , and the position $ r_j $ is not yet occupied in the permutation. If there are no such positions, then we assume that the value of $ r_j $ is not defined. - For all $ t $ from $ 1 $ to $ n $ , we calculate $ count_t $ — the number of positions $ 1 \leq j \leq n $ such that $ r_j $ is defined and $ r_j = t $ . - Consider the positions that are still not occupied by permutation and among those we consider the positions for which the value in the $ count $ array is maximum. - The generator selects one of these positions for the number $ i $ . The generator can choose any position. Let's have a look at the operation of the algorithm in the following example: Let $ n = 5 $ and the algorithm has already arranged the numbers $ 1, 2, 3 $ in the permutation. Consider how the generator will choose a position for the number $ 4 $ : - The values of $ r $ will be $ r = [3, 3, 3, 4, \times] $ , where $ \times $ means an indefinite value. - Then the $ count $ values will be $ count = [0, 0, 3, 1, 0] $ . - There are only two unoccupied positions in the permutation: $ 3 $ and $ 4 $ . The value in the $ count $ array for position $ 3 $ is $ 3 $ , for position $ 4 $ it is $ 1 $ . - The maximum value is reached only for position $ 3 $ , so the algorithm will uniquely select this position for number $ 4 $ . Satisfied with his purchase, Denis went home. For several days without a break, he generated permutations. He believes that he can come up with random permutations no worse than a generator. After that, he wrote out the first permutation that came to mind $ p_1, p_2, \ldots, p_n $ and decided to find out if it could be obtained as a result of the generator. Unfortunately, this task was too difficult for him, and he asked you for help. It is necessary to define whether the written permutation could be obtained using the described algorithm if the generator always selects the position Denis needs.

输入输出格式

输入格式

The first line contains a single integer $ t $ $ (1 \leq t \leq 10^5) $ — the number of test cases. Then the descriptions of the test cases follow. The first line of the test case contains a single integer $ n $ $ (1 \leq n \leq 10^5) $ — the size of the permutation. The second line of the test case contains $ n $ different integers $ p_1, p_2, \ldots, p_n $ ( $ 1 \leq p_i \leq n $ ) — the permutation written by Denis. It is guaranteed that the sum of $ n $ over all test cases doesn't exceed $ 10^5 $ .

输出格式

Print "Yes" if this permutation could be obtained as a result of the generator. Otherwise, print "No". All letters can be displayed in any case.

输入输出样例

输入样例 #1

5
5
2 3 4 5 1
1
1
3
1 3 2
4
4 2 3 1
5
1 5 2 4 3

输出样例 #1

Yes
Yes
No
Yes
No

说明

Let's simulate the operation of the generator in the first test. At the $ 1 $ step, $ r = [1, 2, 3, 4, 5], count = [1, 1, 1, 1, 1] $ . The maximum value is reached in any free position, so the generator can choose a random position from $ 1 $ to $ 5 $ . In our example, it chose $ 5 $ . At the $ 2 $ step, $ r = [1, 2, 3, 4, \times], count = [1, 1, 1, 1, 0] $ . The maximum value is reached in positions from $ 1 $ to $ 4 $ , so the generator can choose a random position among them. In our example, it chose $ 1 $ . At the $ 3 $ step, $ r = [2, 2, 3, 4, \times], count = [0, 2, 1, 1, 0] $ . The maximum value is $ 2 $ and is reached only at the $ 2 $ position, so the generator will choose this position. At the $ 4 $ step, $ r = [3, 3, 3, 4, \times], count = [0, 0, 3, 1, 0] $ . The maximum value is $ 3 $ and is reached only at the $ 3 $ position, so the generator will choose this position. At the $ 5 $ step, $ r = [4, 4, 4, 4, \times], count = [0, 0, 0, 4, 0] $ . The maximum value is $ 4 $ and is reached only at the $ 4 $ position, so the generator will choose this position. In total, we got a permutation of $ 2, 3, 4, 5, 1 $ , that is, a generator could generate it.