Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Roads in Berland

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThere are *n* cities numbered from 1 to *n* in Berland. Some of them are connected by two-way roads. Each road has its own length — an integer number from 1 to 1000. It is known that from each city it is possible to get to any other city by existing roads. Also for each pair of cities it is known the shortest distance between them. Berland Government plans to build *k* new roads. For each of the planned road it is known its length, and what cities it will connect. To control the correctness of the construction of new roads, after the opening of another road Berland government wants to check the sum of the shortest distances between all pairs of cities. Help them — for a given matrix of shortest distances on the old roads and plans of all new roads, find out how the sum of the shortest distances between all pairs of cities changes after construction of each road.

Input

The first line contains integer *n* (2 ≤ *n* ≤ 300) — amount of cities in Berland. Then there follow *n* lines with *n* integer numbers each — the matrix of shortest distances. *j*-th integer in the *i*-th row — *d*_{i, j}, the shortest distance between cities *i* and *j*. It is guaranteed that *d*_{i, i} = 0, *d*_{i, j} = *d*_{j, i}, and a given matrix is a matrix of shortest distances for some set of two-way roads with integer lengths from 1 to 1000, such that from each city it is possible to get to any other city using these roads.

Next line contains integer *k* (1 ≤ *k* ≤ 300) — amount of planned roads. Following *k* lines contain the description of the planned roads. Each road is described by three space-separated integers *a*_{i}, *b*_{i}, *c*_{i} (1 ≤ *a*_{i}, *b*_{i} ≤ *n*, *a*_{i} ≠ *b*_{i}, 1 ≤ *c*_{i} ≤ 1000) — *a*_{i} and *b*_{i} — pair of cities, which the road connects, *c*_{i} — the length of the road. It can be several roads between a pair of cities, but no road connects the city with itself.

Output

Output *k* space-separated integers *q*_{i} (1 ≤ *i* ≤ *k*). *q*_{i} should be equal to the sum of shortest distances between all pairs of cities after the construction of roads with indexes from 1 to *i*. Roads are numbered from 1 in the input order. Each pair of cities should be taken into account in the sum exactly once, i. e. we count unordered pairs.

Examples

Input

2

0 5

5 0

1

1 2 3

Output

3

Input

3

0 4 5

4 0 9

5 9 0

2

2 3 8

1 2 1

Output

17 12

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/18/2017 23:21:10 (c4).

Desktop version, switch to mobile version.

User lists

Name |
---|