Marisa has n×2 mushrooms and she wants to brew n potion bottles, each using exactly 2 mushrooms. If the ith mushroom is paired with the jth mushroom, the resulting potion has a power of Ai,j. Marisa wants to find the combination of mushrooms that maximizes the total power of the n potion bottles.
### Input
- The first line contains an integer n.
- The next n×2 lines, i-th line contains n×2 integers Ai,j. It is guaranteed that Ai,j=Aj,i.
### Output
- Print the maximum total power of n potion bottles.
### Constraints
- 1≤n≤10.
- 0≤|Ai,j|≤106.
### Example
Input:
10−2−20
Output:
−2