Angler's Race

The first line of input contains an integer 'N', the number of fishing spots.
The second line contains three space-separated integers, representing the positions of the three gates.
The third line contains three space-separated integers, representing the number of fishermen waiting at each corresponding gate.

Print a single integer representing the minimum possible total distance.

Since there are only 3 gates, there are only 3! = 6 possible orders to open them. The solution is to simulate the process for all 6 permutations and find the minimum total cost.
For each gate, the fishermen will greedily occupy the closest available spots.

Sample Input 1:

10
4 6 10
5 2 2

Sample Output 1:

10

Explanation for Sample 1:

The original sample output of 18 appears to be incorrect based on the problem's rules. The true minimum is 10. Let's trace the optimal permutation: Gate at 4 -> Gate at 10 -> Gate at 6.
1. Open Gate 4 (5 fishermen):** They need the 5 closest empty spots to 4. These are spots {4, 3, 5, 2, 6}.
- Distances: `|4-4|`=0, `|4-3|`=1, `|4-5|`=1, `|4-2|`=2, `|4-6|`=2.
- Cost for this gate: `0+1+1+2+2 = 6`.
- Spots now occupied: {2, 3, 4, 5, 6}.
2. Open Gate 10 (2 fishermen):** They need the 2 closest empty spots. The remaining spots are {1, 7, 8, 9, 10}. The closest to 10 are {10, 9}.
- Distances: `|10-10|`=0, `|10-9|`=1.
- Cost for this gate: `0+1 = 1`.
- Spots now occupied: {2, 3, 4, 5, 6, 9, 10}.
3. Open Gate 6 (2 fishermen):** They need the 2 closest empty spots. The remaining spots are {1, 7, 8}. The closest to 6 are {7, 8}.
- Distances: `|6-7|`=1, `|6-8|`=2.
- Cost for this gate: `1+2 = 3`.
Total Minimum Cost:** `6 + 1 + 3 = 10`.

Sample Input 2:

20
3 18 12
4 5 3

Sample Output 2:

45

Explanation for Sample 2:

There are 6 permutations of the gates {3, 12, 18}. The optimal order is found by trying them all. For example, the order (3, 12, 18) results in a total distance of 45, which is the minimum.

Expected Time Complexity:

The expected time complexity is O(N * TotalFishermen).

Constraints:

1 <= N <= 1000
1 <= Gate Position <= N
0 <= Fishermen at a gate <= N

Time limit: 1 sec