Problem Description
Given n elements, which have two properties, say Property A and Property B. For convenience, we use two integers Ai and Bi to measure the two properties.
Your task is, to partition the element into two sets, say Set A and Set B , which minimizes the value of max(x∈Set A) {Ax}+max(y∈Set B) {By}.
See sample test cases for further details.
Input
There are multiple test cases, the first line of input contains an integer denoting the number of test cases.
For each test case, the first line contains an integer N, indicates the number of elements. (1 <= N <= 100000)
For the next N lines, every line contains two integers Ai and Bi indicate the Property A and Property B of the ith element. (0 <= Ai, Bi <= 1000000000)
Output
For each test cases, output the minimum value.
Sample Input
1
3
1 100
2 100
3 1
Sample Output
Case 1: 3
