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
sys.setrecursionlimit(10**9)
n=int(input())
Cost=[]
s1,s2=0,0
for i in range(n):
    a,b=map(int,input().split())
    s1+=a
    s2+=b
    Cost.append([a,i])
    Cost.append([b,i])
Cost.sort()
s3=sum([Cost[i][0] for i in range(n)])
if len(set([Cost[i][1] for i in range(n)]))==n:
    if Cost[n-1][1]==Cost[n][1]:
        s3+=min(Cost[n+1][0]-Cost[n-1][0],Cost[n][0]-Cost[n-2][0])
    else:
        s3+=Cost[n][0]-Cost[n-1][0]
print(min(s1,s2,s3))