Relay

JOI High School's track club has $N$ members, numbered from 1 to $N$. Member $i$ ($1 \le i \le N$) runs the 100 m sprint in $A_i$ msec, and has baton control ability $B_i$.

The club will enter the 300 m relay at a national contest. Three members each run 100 m, and each runner passes the baton to the next. If the first runner is $i$, the second is $j$, and the third is $k$ ($1 \le i, j, k \le N$), the relay goes as follows.

1. Runner $i$ runs 100 m, taking $A_i$ msec.
2. Runner $i$ passes the baton to runner $j$, taking $\max(B_i, B_j)$ msec.
3. Runner $j$ runs 100 m, taking $A_j$ msec.
4. Runner $j$ passes the baton to runner $k$, taking $\max(B_j, B_k)$ msec.
5. Runner $k$ runs 100 m, taking $A_k$ msec.

The record is therefore

$A_i + \max(B_i, B_j) + A_j + \max(B_j, B_k) + A_k$

As the coach, you choose three distinct members and decide their running order so that the record is as small as possible. Write a program that finds the minimum possible record for the 300 m relay.

The first line contains $N$. Each of the next $N$ lines contains $A_i$ and $B_i$, separated by a space.

Print one integer on a single line: the minimum possible record of the 300 m relay, in msec.

• $3 \le N \le 200\,000$
• $1 \le A_i \le 10^8$ ($1 \le i \le N$)
• $1 \le B_i \le 10^8$ ($1 \le i \le N$)