[ICPC 2022 Jinan R] Stack Sort

Luogu

IDLGP9677

Time1000ms

Memory512MB

DifficultyP2

2022O2优化ICPC济南

You are given a permutation with $n$ numbers, $a_1, a_2, \dots, a_n (1\leq a_i\leq n, a_i\neq a_j\textrm{ when }i\neq j)$. You want to sort these numbers using $m$ stacks. Specifically, you should complete the following task: Initially, all stacks are empty. You need to push each number $a_i$ to the top of one of the $m$ stacks one by one, in the order of $a_1,a_2,\ldots, a_n$. $\textbf{After pushing all numbers in the stacks}$, you pop all the elements from the stacks in a clever order so that the first number you pop is $1$, the second number you pop is $2$, and so on. **If you pop an element from a stack $S$, you cannot pop any element from the other stacks until $S$ becomes empty.** What is the minimum possible $m$ to complete the task? ## Input The first line contains one integer $T~(1\le T \le 10^5)$, the number of test cases. For each test case, the first line contains one positive integer $n~(1\le n \le 5 \times 10^5)$. The next line contains $n$ integers $a_1,\ldots, a_n~(1 \le a_i\le n)$ denoting the permutation. It is guaranteed that $a_1,\ldots, a_n$ form a permutation, i.e. $a_i\neq a_j$ for $i \neq j$. It is guaranteed that the sum of $n$ over all test cases is no more than $5\times 10^5$. ## Output For each test case, output the minimum possible $m$ in one line. [samples]

Samples

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API Response (JSON)

{
  "problem": {
    "name": "[ICPC 2022 Jinan R] Stack Sort",
    "description": {
      "content": "You are given a permutation with $n$ numbers, $a_1, a_2, \\dots, a_n (1\\leq a_i\\leq n, a_i\\neq a_j\\textrm{ when }i\\neq j)$.  You want to sort these numbers using $m$ stacks. Specifically, you should c",
      "description_type": "Markdown"
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    "platform": "Luogu",
    "limit": {
      "time_limit": 1000,
      "memory_limit": 524288
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    "difficulty": {
      "LuoguStyle": "P2"
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    "is_remote": true,
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    "sign": "LGP9677"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a permutation with $n$ numbers, $a_1, a_2, \\dots, a_n (1\\leq a_i\\leq n, a_i\\neq a_j\\textrm{ when }i\\neq j)$. \n\nYou want to sort these numbers using $m$ stacks. Specifically, you should c...",
      "is_translate": false,
      "language": "English"
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