Problem Background

A straight flush refers to a set of poker cards that are of the same suit and have consecutive numbers.

Problem Description

I currently have $n$ poker cards, but they may not form a straight flush. I want to know the minimum number of cards I need to replace to make these $n$ cards form a straight flush.

Input Format

The first line contains an integer $n$, representing the number of poker cards.

The next $n$ lines each contain two integers $a_i$ and $b_i$. $a_i$ represents the suit of the $i$-th card, and $b_i$ represents the number of the $i$-th card.

Output Format

A single line containing an integer, representing the minimum number of cards that need to be replaced to achieve the goal.

Sample Input and Output

Sample Input #1

5
1 1
1 2
1 3
1 4
1 5

Sample Output #1

0

Sample Input #2

5
1 9
1 10
2 11
2 12
2 13

Sample Output #2

2

Notes

• For $30\%$ of the data, $n \le 10$;
• For $60\%$ of the data, $n \le 10^5$, $1 \le a_i \le 10^5$, $1 \le b_i \le n$;
• For $100\%$ of the data, $n \le 10^5$, $1 \le a_i, b_i \le 10^9$;

见题面 Input 部分

见题面 Output 部分