Problem Statement

AtCoDeer the deer found $N$ rectangle lying on the table, each with height $1$. If we consider the surface of the desk as a two-dimensional plane, the $i$-th rectangle $i(1≤i≤N)$ covers the vertical range of \[i-1,i\] and the horizontal range of \[l_i,r_i\], as shown in the following figure:

AtCoDeer will move these rectangles horizontally so that all the rectangles are connected. For each rectangle, the cost to move it horizontally by a distance of $x$, is $x$. Find the minimum cost to achieve connectivity. It can be proved that this value is always an integer under the constraints of the problem.

Constraints

• All input values are integers.
• $1≤N≤10^5$
• $1≤l_i<r_i≤10^9$

Partial Score

• $300$ points will be awarded for passing the test set satisfying $1≤N≤400$ and $1≤l_i<r_i≤400$.

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Input

The input is given from Standard Input in the following format:

$N$ $l_1$ $r_1$ $l_2$ $r_2$ : $l_N$ $r_N$

Output

Print the minimum cost to achieve connectivity.

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Sample Input 1

3
1 3
5 7
1 3

Sample Output 1

2

The second rectangle should be moved to the left by a distance of $2$.

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Sample Input 2

3
2 5
4 6
1 4

Sample Output 2

0

The rectangles are already connected, and thus no move is needed.

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Sample Input 3

5
999999999 1000000000
1 2
314 315
500000 500001
999999999 1000000000

Sample Output 3

1999999680

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Sample Input 4

5
123456 789012
123 456
12 345678901
123456 789012
1 23

Sample Output 4

246433

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Sample Input 5

1
1 400

Sample Output 5

0