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
import bisect
n = int(input())
ab = [list(map(int,input().split())) for i in range(n)]
both = []
for i in range(n):
  both.extend(ab[i])
both.sort()
ans = 10**18
sm = sum(both[:n])
for i in range(n):
  ai = bisect.bisect_left(both,ab[i][0])
  bi = bisect.bisect_left(both,ab[i][1])
  if ai < n and bi < n:
    ans = min(ans,sm)
  elif ai < n-1:
    ans = min(ans,sm-both[n-1]+ab[i][1])
  elif ai == n-1:
    ans = min(ans,sm-both[n-2]+ab[i][1])
  elif bi < n-1:
    ans = min(ans,sm-both[n-1]+ab[i][0])
  elif bi == n-1:
    ans = min(ans,sm-both[n-2]+ab[i][0])
  else:
    ans = min(ans,sm-both[n-1]-both[n-2]+sum(ab[i]))
a,b = list(zip(*ab))
ans = min(ans,sum(a),sum(b))
print(ans)