Score : $450$ points

问题陈述

在某国家有 $N$ 个城市。
你将从城市 1 的办公室出发，经过零个或多个城市到达城市 $N$ 的目的地。
有两种交通工具可供选择：公司汽车和火车。从城市 $i$ 到城市 $j$ 所需的时间如下：

• 乘坐公司汽车所需时间为 $D_{i,j} \times A$ 分钟，
• 乘坐火车所需时间为 $D_{i,j} \times B + C$ 分钟。

你可以从公司汽车换乘到火车，但不能反过来。
你可以在不花费时间的情况下进行换乘，但只能在城市中进行。

请问从城市 1 到城市 $N$ 的最短旅行时间是多少分钟？

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

There are $N$ cities in a certain country.
You will travel from your office in city $1$ to a destination in city $N$, via zero or more cities.
Two types of transportation are available: company car and train. The time required to travel from city $i$ to city $j$ is as follows:

• $D_{i,j} \times A$ minutes by company car, and
• $D_{i,j} \times B + C$ minutes by train.

You can switch from company car to train, but not vice versa.
You can do so without spending time, but only in a city.

What is the minimum time in minutes to travel from city $1$ to city $N$?

Constraints

• $2 \leq N \leq 1000$
• $1 \leq A, B, C \leq 10^6$
• $D_{i,j} \leq 10^6$
• $D_{i,i} = 0$
• $D_{i,j} = D_{j,i} > 0$ $(i \neq j)$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

$N$ $A$ $B$ $C$

$D_{1,1}$ $D_{1,2}$ $\ldots$ $D_{1,N}$

$D_{2,1}$ $D_{2,2}$ $\ldots$ $D_{2,N}$

$\vdots$

$D_{N,1}$ $D_{N,2}$ $\ldots$ $D_{N,N}$

Output

Print the answer as an integer.

Sample Input 1

4 8 5 13
0 6 2 15
6 0 3 5
2 3 0 13
15 5 13 0

Sample Output 1

78

You can travel from city $1$ to city $4$ in a total of $78$ minutes by moving as follows.

• Travel by company car from city $1$ to city $3$. This takes $2 \times 8 = 16$ minutes.
• Travel by company car from city $3$ to city $2$. This takes $3 \times 8 = 24$ minutes.
• Travel by train from city $2$ to city $4$. This takes $5 \times 5 + 13 = 38$ minutes.

It is impossible to travel from city $1$ to city $4$ in less than $78$ minutes.

Sample Input 2

3 1 1000000 1000000
0 10 1
10 0 10
1 10 0

Sample Output 2

1

Sample Input 3

5 954257 954213 814214
0 84251 214529 10017 373342
84251 0 91926 32336 164457
214529 91926 0 108914 57762
10017 32336 108914 0 234705
373342 164457 57762 234705 0

Sample Output 3

168604826785

update @ 2024/3/10 01:48:18