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?

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.

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.

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

见题面 Input 部分

见题面 Output 部分