Recently, Uncle Fyodor read in the Murzilka magazine that the highest waterfall in the world — This is the Angel Falls, whose height is 1054 meters. “It would be great to see such a waterfall!”, — he dreamed.
But Venezuela is far away, so for now Uncle Fyodor decided to start by exploring the Smetanka River, which flows next to Prostokvashino. It starts in the hills and gradually descends towards the village. Uncle Fyodor, together with Sharik, walked along the entire course of Smetanka from its source. Sometimes along the way they met waterfalls. As Uncle Fyodor learned from that article in Murzilka, a section of a river with a constant slope angle exceeding 45 degrees, that is, a section whose height is greater than its length, is considered a waterfall.
Already after the trip, over and over again redrawing the map of Smetanka on paper, Uncle Fyodor noticed that if you draw a side view of Smetanka (that is, the higher the point — is drawn, the higher it is above sea level, and the more to the right — the farther it is from the source and closer to Prostokvashino), then we get a non-increasing broken line, which is very easy to analyze. Each segment of this broken line — this is just a section of the river with a constant angle of inclination, which may turn out to be a waterfall!
After spending several evenings studying the Smetanka map, Uncle Fyodor remembered that in addition to waterfalls, there are also cascades of waterfalls. A waterfall cascade is one or more successive waterfalls. Cascade height — is the difference between the heights of the highest and lowest points belonging to this cascade.
Now Uncle Fedor was wondering, what is the height of the highest cascade of waterfalls on Smetanka? Help him: according to the description of the river made by Sharik and Uncle Fyodor, find this number.
Input
The first line contains the number n (2<=n<=10
5 ) — the number of vertices of the broken line describing the Smetanka river. The next n lines contain the coordinates of these points, the i-th line contains numbers x
i and y
i — horizontal distance from the point to the source and the height of the point above sea level (0x
i<=10
9, y
i<=10< sup>9 ). The points are listed starting from the source of the river, that is, starting from a point whose x-coordinate is zero and whose y-coordinate is — maximum among all points. It is guaranteed that the river flows from top to bottom and from left to right, that is, each next point is neither higher nor to the left of the previous one.
Imprint
Print one integer: the height of the highest cascade of waterfalls on this river. If the river doesn't actually have waterfalls, print 0.
Examples
| # |
Input |
Output |
| 1 |
3
0 15
1 10
5 5 |
10 |