题目描述
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Limak is a brown bear.
Brown bears often climb trees and so does Limak.
As you probably know, bears use ropes to move between tops of trees.
There are N trees in a row.
i-th of them grows at coordinate X[i] and has height H[i].
A further tree is always higher - it's guaranteed that X[i] < X[i+1] and H[i] < H[i+1].
Limak is currently at the top of the first tree and he has a rope of length L.
He wants to be at the top of the last tree.
He can move from a-th to b-th tree if and only if all tree conditions are fulfilled:
1) a < b
2) (X[b]-X[a])^2 + (H[b]-H[a])^2 ≤ L - rope must be long enough
3) H[b]-H[a] < X[b]-X[a] - it's not safe to go very uphill
Note that there is no square root in the second condition.
The reason is that bears calculate distances a bit different than people.
Limak doesn't know if his rope is long enough.
Could you help him and calculate the minimum L for which he can get from the first tree to the last one?
Print -1 instead if there is no L for which Limak would reach the last tree.
Input format:
The first line contains one integer number N, denoting number of trees.
i-th of the next N lines contains two integer numbers X[i] and H[i], describing i-th tree.
Output format:
In the single line print the minimum possible L for which Limak would be able to get from the first to the last tree.
If there is no such L, print -1 instead.
Constraints:
2 ≤ N ≤ 10^6
1 ≤ X[i], H[i] ≤ 10^7
X[i] < X[i+1]
H[i] < H[i+1]
SAMPLE INPUT
4
3 2
4 3
13 4
15 5
SAMPLE OUTPUT
104
Explanation
Limak can't go to the second tree because inequality H[2]-H[1] < X[2]-X[1] doesn't hold.
With rope of length at least 10^2 + 2^2 = 104 he can go from the first to the third tree.
Then he needs rope of length at least 2^2 + 1^2 = 5 to get to the last tree.
So he can reach the last tree with L = 104.
Limak can also skip a third tree and go directly to the last one but he would need L = 12^2+3^2 = 153.
输入格式
见题面
输出格式
见题面