???题目6 : Cake

题目6 : Cake

时间限制:1000ms

单点时限:1000ms

内存限制:256MB

描述

To celebrate that WF-2018 will be held in PKU, Alice, Bob, and Cate are asked to make

N cakes.

Every cake i needs to go through 3 steps in restrict order:

1. Alice mixes flour and water for ai minutes;

2. Bob carefully bakes it for bi minutes;

3. Cate makes cream decoration for ci minutes.

Since Cate wants to have different kinds of cakes, the third step of any cake i is always not less time-consuming than the second step of any cake j. Also, it is reasonable that once anyone starts to process a cake, the procedure cannot be stopped then be resumed.

To have these cakes done as soon as possible, they need your help.

输入

There are several cases (less than 15 cases).

The first line of every case contains an integer N (1 ≤ N ≤ 105)—the number of cakes to prepare.

After that, N lines follow, each of them contains three integers ai, bi and ci (1 ≤ i ≤ N; 0 <ai, bi, ci < 106)—time that needs to be spent on the three steps of cake i respectively.

It is guaranteed that for any i and any j, bi is no greater than cj.

The input ends with N = 0.

输出

For every case, print in a single line the least possible time to make all cakes.

样例提示

One of the optimal solutions is to have Alice and Bob process cakes in order of 2, 3, 1, while Cate processes cakes in order of 2, 1, 3.

样例输入

35 3 43 2 93 4 80

样例输出

26

比赛已经结束，去题库提交。