Ekiden Race

AtCoder

IDarc162_a

Time2000ms

Memory256MB

Difficulty—

There are $N$ people, numbered from $1$ to $N$, who participated in a round-trip race between two points. The following information is recorded about this race. * The **outward** times of any two people were different, and person $i$ $(1 \leq i \leq N)$ had the $i$\-th fastest outward time. * The **round-trip** times (the sum of the outward and return times) of any two people were different, and person $i$ $(1 \leq i \leq N)$ had the $P_i$\-th fastest round-trip time. * The person (or persons) with the fastest **return** time was awarded the **fastest return award**. Here, $P_1, P_2, \dots, P_N$ is a permutation of $1, 2, \dots, N$. How many people could have received the **fastest return award**? There are $T$ test cases. Answer each of them. ## Constraints * $1 \leq T \leq 500$ * $2 \leq N \leq 10^3$ * $P_1, P_2, \dots, P_N$ is a permutation of $1, 2, \dots, N$. * All input values are integers. * The sum of $N$ over all test cases in a single input is at most $10^3$. ## Input The input is given from Standard Input in the following format: $T$ $\mathrm{case}_1$ $\vdots$ $\mathrm{case}_T$ Each test case, $\mathrm{case}_i\ (1 \leq i \leq T)$, is given in the following format: $N$ $P_1$ $P_2$ $\cdots$ $P_N$ [samples]

Samples

Input #1

3
2
2 1
4
1 2 3 4
20
13 2 7 1 5 9 3 4 12 10 15 6 8 14 20 16 19 18 11 17

Output #1

1
4
7

*   In the first test case, two people participated in the race, and person $2$ overtook person $1$ on the return leg. In this case, the fastest return award is awarded to person $2$.
*   In the second test case, the rankings did not change on the return leg, so any person could have received the fastest return award.

API Response (JSON)

{
  "problem": {
    "name": "Ekiden Race",
    "description": {
      "content": "There are $N$ people, numbered from $1$ to $N$, who participated in a round-trip race between two points. The following information is recorded about this race. *   The **outward** times of any two p",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc162_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ people, numbered from $1$ to $N$, who participated in a round-trip race between two points. The following information is recorded about this race.\n\n*   The **outward** times of any two p...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments