Problem Statement

There are $N$ cards, each with a number written on both sides. On the $i$-th card, the number $A_i$ is written in red on one side, and the number $B_i$ is written in blue on the other side. Initially, all cards are placed with the red number side facing up. Alice and Bob play a game in which they repeat the following steps.

• First, Alice chooses one of the remaining cards and flips it over. Next, Bob removes one of the remaining cards. Then, Bob scores points equal to the number written on the face-up side of the removed card.

The game ends when there are no cards left.

Alice tries to minimize Bob's score at the end of the game, and Bob tries to maximize it. What is Bob's score at the end of the game when both players take optimal steps?

Constraints

• $1\leq N\leq 2\times 10^5$
• $1\leq A_i, B_i\leq 10^9$ $(1\leq i \leq N)$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N
A_1 B_1
A_2 B_2
\vdots
A_N B_N

Output

Print the answer as an integer.