Pairing Wizards

AtCoder

IDarc142_e

Time2000ms

Memory256MB

Difficulty—

There are $N$ wizards, numbered $1, \ldots, N$. Wizard $i$ has a strength of $a_i$ and plans to defeat a monster with a strength of $b_i$. You can perform the following operation any number of times. * Increase the strength of any wizard of your choice by $1$. A pair of Wizard $i$ and Wizard $j$ (let us call this pair $(i, j)$) is said to be **good** when at least one of the following conditions is satisfied. * Wizard $i$ has a strength of at least $b_i$ and Wizard $j$ has a strength of at least $b_j$. * Wizard $i$ has a strength of at least $b_j$ and Wizard $j$ has a strength of at least $b_i$. Your objective is to make the pair $(x_i, y_i)$ good for every $i=1, \ldots, M$. Find the minimum number of operations needed to achieve it. ## Constraints * $2 \leq N \leq 100$ * $1 \leq a_i,b_i \leq 100$ * $1 \leq M \leq \frac{N(N-1)}{2}$ * $1 \leq x_i \lt y_i \leq N$ * $(x_i,y_i) \neq (x_j,y_j)$, if $i\neq j$. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $a_1$ $b_1$ $\vdots$ $a_N$ $b_N$ $M$ $x_1$ $y_1$ $\vdots$ $x_M$ $y_M$ [samples]

Samples

Input #1

Output #1

2

You can perform the operation once for Wizard $1$ and once for Wizard $4$ to achieve the objective with the fewest operations.

Input #2

Output #2

0

No operation is needed.

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Pairing Wizards",
    "description": {
      "content": "There are $N$ wizards, numbered $1, \\ldots, N$.   Wizard $i$ has a strength of $a_i$ and plans to defeat a monster with a strength of $b_i$. You can perform the following operation any number of times",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc142_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ wizards, numbered $1, \\ldots, N$.  \nWizard $i$ has a strength of $a_i$ and plans to defeat a monster with a strength of $b_i$.\nYou can perform the following operation any number of times...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments