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Language: Terrible Sets
Description Let N be the set of all natural numbers {0 , 1 , 2 , . . . }, and R be the set of all real numbers. wi, hi for i = 1 . . . n are some elements in N, and w0 = 0.
Define set B = {< x, y > | x, y ∈ R and there exists an index i > 0 such that 0 <= y <= hi ,∑ _{0<=j<=i-1}wj <= x <= ∑_{0<=j<=i}wj}
Again, define set S = {A| A = WH for some W , H ∈ R ^{+} and there exists x0, y0 in N such that the set T = { < x , y > | x, y ∈ R and x0 <= x <= x0 +W and y0 <= y <= y0 + H} is contained in set B}.
Your mission now. What is Max(S)? Wow, it looks like a terrible problem. Problems that appear to be terrible are sometimes actually easy. But for this one, believe me, it's difficult. Input The input consists of several test cases. For each case, n is given in a single line, and then followed by n lines, each containing wi and hi separated by a single space. The last line of the input is an single integer -1, indicating the end of input. You may assume that 1 <= n <= 50000 and w _{1}h_{1}+w_{2}h_{2}+...+w_{n}h_{n} < 10^{9}.Output Simply output Max(S) in a single line for each case. Sample Input 3 1 2 3 4 1 2 3 3 4 1 2 3 4 -1 Sample Output 12 14 Source |

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