Given three sequences $A$, $B$, and $C$, each consisting of $n$ elements. Find three indices $1 \le i, j, k \le n$ such that $|A_i - B_j| + |B_j - C_k| + |C_k - A_i|$ is minimized.
### Input
- The first line contains an integer $n$.
- The second line contains $n$ integers $A_i$.
- The third line contains $n$ integers $B_i$.
- The fourth line contains $n$ integers $C_i$.
### Output
- Print an integer, the minimum value of $|A_i - B_j| + |B_j - C_k| + |C_k - A_i|$.
### Constraints
- $1 \le n \le 10^5$.
- $1 \le A_i, B_i, C_i \le 10^9$.
### Example
Input:
```
3
4 2 5
3 2 1
5 5 5
```
Output:
```
4
```
