Count Median

AtCoder

IDabc169_e

Time2000ms

Memory256MB

Difficulty—

There are $N$ integers $X_1, X_2, \cdots, X_N$, and we know that $A_i \leq X_i \leq B_i$. Find the number of different values that the median of $X_1, X_2, \cdots, X_N$ can take. ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $1 \leq A_i \leq B_i \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $B_1$ $A_2$ $B_2$ $:$ $A_N$ $B_N$ [samples] ## Notes The median of $X_1, X_2, \cdots, X_N$ is defined as follows. Let $x_1, x_2, \cdots, x_N$ be the result of sorting $X_1, X_2, \cdots, X_N$ in ascending order. * If $N$ is odd, the median is $x_{(N+1)/2}$; * if $N$ is even, the median is $(x_{N/2} + x_{N/2+1}) / 2$.

Samples

Input #1

2
1 2
2 3

Output #1

3

*   If $X_1 = 1$ and $X_2 = 2$, the median is $\frac{3}{2}$;
    
*   if $X_1 = 1$ and $X_2 = 3$, the median is $2$;
    
*   if $X_1 = 2$ and $X_2 = 2$, the median is $2$;
    
*   if $X_1 = 2$ and $X_2 = 3$, the median is $\frac{5}{2}$.
    

Thus, the median can take three values: $\frac{3}{2}$, $2$, and $\frac{5}{2}$.

Input #2

3
100 100
10 10000
1 1000000000

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Count Median",
    "description": {
      "content": "There are $N$ integers $X_1, X_2, \\cdots, X_N$, and we know that $A_i \\leq X_i \\leq B_i$. Find the number of different values that the median of $X_1, X_2, \\cdots, X_N$ can take.",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc169_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ integers $X_1, X_2, \\cdots, X_N$, and we know that $A_i \\leq X_i \\leq B_i$. Find the number of different values that the median of $X_1, X_2, \\cdots, X_N$ can take.\n\n## Constraints\n\n*   ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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