Find Point Illuminated by Most Lamps

A lamp (x,r) lights the closed interval [x−r,x+r], with r>0. Return the position lit by the most lamps at once; if several positions tie, take the smallest coordinate.

This site has made the standard input and output explicit.

输入格式

The first line contains n, followed by n lines of x r. On this site 1≤n≤200000, −10⁹≤x≤10⁹, 1≤r≤10⁹.

输出格式

Output one integer, the answer.

样例 1

输入：

3
-2 3
2 3
2 1

输出：

1

样例 2

输入：

2
-2 1
2 1

输出：

-3

样例 3

输入：

2
0 1
2 1

输出：

1

样例说明

Example 1: the only position shared by all three lamps is 1. Example 2: at most one lamp lights any position, and the leftmost such position is −3. Example 3: the two segments meet at the closed endpoint 1, which is lit by both lamps, so the answer is 1.