Roller Coaster Railroad

Anna is working in an amusement park and she is in charge of building the railroad for a new roller coaster. She has already designed $n$ special sections (conveniently numbered from $0$ to $n-1$ that affect the speed of a roller coaster train. She now has to put them together and propose a final design of the roller coaster. For the purpose of this problem you may assume that the length of the train is zero.

For each $i$ between $0$ and $n-1$, inclusive, the special section has two properties:

• when entering the section, there is a speed limit: the speed of the train must be less or equal to $s_i$ km/h (kilometers per hour),

• when leaving the section, the speed of the train is exactly $t_i$ km/h, regardless of the speed at which the train entered the section.

The finished roller coaster is a single railroad line that contains the $n$ special sections in some order. Each of the $n$ sections should be used exactly once. Consecutive sections are connected with tracks. Anna should choose the order of the $n$ sections and then decide the lengths of the tracks. The length of a track is measured in meters and may be equal to any non-negative integer (possibly zero).

Each meter of the track between two special sections slows the train down by $1$ km/h. At the beginning of the ride, the train enters the first special section in the order selected by Anna, going at $1$ km/h.

The final design must satisfy the following requirements:

• the train does not violate any speed limit when entering the special sections;

• the speed of the train is positive at any moment.

Your task is to find the minimum possible total length of tracks between sections.

Input

First line contains number $n(2\le n\le 2\cdot 10^5)$. Each of the next $n$ lines contains numbers $s_i$ and $t_i(1\le i\le n,1\le s_i,t_i\le 10^9)$.

Output

Print the minimum possible total length of all tracks between sections.

Examples