Mirko's Pizza Scheduling

Mirko's Pizza Shop is the best in town. Every resident enjoys his pizza for lunch. Although the delivery is extremely fast (nearly instantaneous), Mirko only has a single small oven that can bake one pizza at a time.

There are \( N \) residents numbered from 1 to \( N \). The i-th resident plans to have lunch at time \( L_i \) and his pizza requires \( T_i \) time units to bake.

If a resident receives his pizza \( K \) time units before \( L_i \), Mirko earns \( K \) dollars in tip. Conversely, if the pizza is delivered \( K \) time units after \( L_i \), Mirko must pay the resident \( K \) dollars. Delivering the pizza exactly on time results in neither a tip nor a penalty.

Help Mirko arrange the baking order for the day so that his total tip is maximized.

Note:

• The day starts at time 0 and is infinitely long.
• Residents may change their \( T_i \) and \( L_i \) over time.

inputFormat

The first line contains a single integer \( N \), the number of residents.

Each of the following \( N \) lines contains two integers \( T_i \) and \( L_i \), which represent the baking time and planned lunch time of the i-th resident respectively.

outputFormat

Output a single integer, the maximum total tip Mirko can obtain by optimally scheduling the baking order.

sample

3
6 10
8 15
5 12

2