Set Merging

AtCoder

IDagc055_e

Time3000ms

Memory256MB

Difficulty—

You have $N$ sets $S_1, S_2, \ldots, S_N$. Initially, for each $i$ from $1$ to $N$, set $S_i$ contains only integer $i$ (that is, $S_i = {i}$). You are allowed to perform the following operation: * Choose any $i$ with $1 \le i \le N-1$. Let $U = S_i \cup S_{i+1}$ ー the union of sets $S_i$ and $S_{i+1}$. Then, replace both $S_i$ and $S_{i+1}$ with $U$. You want to perform a finite number of operations above (maybe zero), to get a configuration, in which $S_i = {L_i, L_i+1, \ldots, R_i-1, R_i}$ for all $i$ from $1$ to $N$. Is it possible to reach this configuration? If it is possible, also find the smallest number of operations needed to reach it. ## Constraints * $1 \le N \le 5\cdot 10^5$ * $1 \le L_i \le R_i \le N$ ## Input Input is given from Standard Input in the following format: $N$ $L_1$ $R_1$ $L_2$ $R_2$ $\vdots$ $L_N$ $R_N$ [samples]

Samples

Input #1

Output #1

\-1

It can be proved that it's impossible to obtain the required configuration.

Input #2

Output #2

4

We can perform the following sequence of operations:

*   Choose $i = 2$, get $S_1 = {1}, S_2 = {2, 3}, S_3 = {2, 3}, S_4 = {4}$
*   Choose $i = 1$, get $S_1 = {1, 2, 3}, S_2 = {1, 2, 3}, S_3 = {2, 3}, S_4 = {4}$
*   Choose $i = 3$, get $S_1 = {1, 2, 3}, S_2 = {1, 2, 3}, S_3 = {2, 3, 4}, S_4 = {2, 3, 4}$
*   Choose $i = 2$, get $S_1 = {1, 2, 3}, S_2 = {1, 2, 3, 4}, S_3 = {1, 2, 3, 4}, S_4 = {2, 3, 4}$

API Response (JSON)

{
  "problem": {
    "name": "Set Merging",
    "description": {
      "content": "You have $N$ sets $S_1, S_2, \\ldots, S_N$. Initially, for each $i$ from $1$ to $N$, set $S_i$ contains only integer $i$ (that is, $S_i = {i}$). You are allowed to perform the following operation: *  ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc055_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You have $N$ sets $S_1, S_2, \\ldots, S_N$. Initially, for each $i$ from $1$ to $N$, set $S_i$ contains only integer $i$ (that is, $S_i = {i}$).\nYou are allowed to perform the following operation:\n\n*  ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments