Social Circles

Problem Description

There are $N$ people. Each person does not want others to sit too close, so he wants $L_i$ empty chairs on his left and $R_i$ empty chairs on his right; each person himself occupies $1$ chair.

Now they will sit in several circles. What is the minimum number of chairs needed (including the chairs each person sits on)?

Input Format

The first line contains an integer $N$.

Lines $2$ to $N+1$ each contain two integers $L_i$ and $R_i$.

Output Format

One integer: the minimum number of chairs needed.

Sample Input

4
1 2
2 1
3 5
5 3

Sample Output

15

Constraints

$1 \le N \le 1 \times 10^5$.

$0 \le L_i, R_i \le 1 \times 10^9$.