Travelling Salesman Problem

There are n cities numbered from 1 to n, and city i has beauty a_i.

A salesman wants to start at city 1, visit every city exactly once, and return to city 1.

For all i≠ j, a flight from city i to city j costs max(c_i,a_j-a_i) dollars, where c_i is the price floor enforced by city i. Note that there is no absolute value. Find the minimum total cost for the salesman to complete his trip.

Input

The first line contains a single integer n (2≤ n≤ 10^5) — the number of cities.

The i-th of the next n lines contains two integers a_i, c_i (0≤ a_i,c_i≤ 10^9) — the beauty and price floor of the i-th city.

Output

Output a single integer — the minimum total cost.

Examples

Input

3 1 9 2 1 4 1

Output

11

Input

6 4 2 8 4 3 0 2 3 7 1 0 1

Output

13

Note

In the first test case, we can travel in order 1→ 3→ 2→ 1.

• The flight 1→ 3 costs max(c_1,a_3-a_1)=max(9,4-1)=9.
• The flight 3→ 2 costs max(c_3, a_2-a_3)=max(1,2-4)=1.
• The flight 2→ 1 costs max(c_2,a_1-a_2)=max(1,1-2)=1.

The total cost is 11, and we cannot do better.

inputFormat

Input

The first line contains a single integer n (2≤ n≤ 10^5) — the number of cities.

The i-th of the next n lines contains two integers a_i, c_i (0≤ a_i,c_i≤ 10^9) — the beauty and price floor of the i-th city.

outputFormat

Output

Output a single integer — the minimum total cost.

Examples

Input

3 1 9 2 1 4 1

Output

11

Input

6 4 2 8 4 3 0 2 3 7 1 0 1

Output

13

Note

In the first test case, we can travel in order 1→ 3→ 2→ 1.

• The flight 1→ 3 costs max(c_1,a_3-a_1)=max(9,4-1)=9.
• The flight 3→ 2 costs max(c_3, a_2-a_3)=max(1,2-4)=1.
• The flight 2→ 1 costs max(c_2,a_1-a_2)=max(1,1-2)=1.

The total cost is 11, and we cannot do better.

样例

3
1 9
2 1
4 1

11

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