Min Cost Cycle

We have a directed weighted graph with N vertices. Each vertex has two integers written on it, and the integers written on Vertex i are A_i and B_i.

In this graph, there is an edge from Vertex x to Vertex y for all pairs 1 \leq x,y \leq N, and its weight is {\rm min}(A_x,B_y).

We will consider a directed cycle in this graph that visits every vertex exactly once. Find the minimum total weight of the edges in such a cycle.

Constraints

• 2 \leq N \leq 10^5
• 1 \leq A_i \leq 10^9
• 1 \leq B_i \leq 10^9
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N A_1 B_1 A_2 B_2 : A_N B_N

Output

Print the minimum total weight of the edges in such a cycle.

Examples

Input

3 1 5 4 2 6 3

Output

7

Input

4 1 5 2 6 3 7 4 8

Output

10

Input

6 19 92 64 64 78 48 57 33 73 6 95 73

Output

227

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N A_1 B_1 A_2 B_2 : A_N B_N

outputFormat

Output

Print the minimum total weight of the edges in such a cycle.

Examples

Input

3 1 5 4 2 6 3

Output

7

Input

4 1 5 2 6 3 7 4 8

Output

10

Input

6 19 92 64 64 78 48 57 33 73 6 95 73

Output

227

样例

3
1 5
4 2
6 3

7