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
n=int(input())
a=[]
b=[]
for i in range(n):
    p,q=map(int,input().split())
    a.append((p,i,0))
    a.append((q,i,1))
a.sort(key=lambda x:x[0])
result=0
l=[0]*n
flag=0
for i in range(n):
    if l[a[i][1]]==1:
        flag=1
        break
    else:
        l[a[i][1]]=1
t=a[0][2]
s=0
for i in range(n):
    s+=a[i][2]-a[0][2]
if s==0:
    flag=1
if flag==1:

    for i in range(n):
        result+=a[i][0]
    print(result)
else:
    if a[n-1][1]==a[n][1]:
        for i in range(n):
            result+=a[i][0]
        result+=min(a[n+1][0]-a[n-1][0],a[n][0]-a[n-2][0])
        print(result)
    else:
        for i in range(n):
            result+=a[i][0]
        result+=a[n][0]-a[n-1][0]
        print(result)