Terrible Sets

Time Limit: 1 Second    Memory Limit: 32768 KB

Let N be the set of all natural numbers {0, 1, 2, ... }, and R be the set of all real numbers. w_i, h_i for i = 1 ... n are some elements in N, and w₀ = 0.

Define set B = { | x, y R and there exists an index i > 0 such that 0 <= y <= h_i, }

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 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 w_i and h_i 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 w₁h₁+w₂h₂+...+w_nh_n < 10⁹.

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

Submit

Source: Asia 2004, Shanghai (Mainland China), Preliminary