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
import sys;input=sys.stdin.readline;N=int(input());A=[-1]*N;B=[-1]*N
for i in range(N):
    A[i],B[i]=map(int,input().split())
ans=min(sum(A),sum(B));temp=[(A[i],i) for i in range(N)]+[(B[i],i) for i in range(N)];temp.sort();data=[0]*N
for i in range(N):data[temp[i][1]]+=1
S=sum(temp[i][0] for i in range(N))
if max(data)==2:
    print(S)
else:
    for i in range(N):ans=min(ans,S+max(A[i],B[i])-temp[N-1-(temp[N-1][1]==i)][0]);
    print(ans)
