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())
b = []
ASUM = 0
BSUM = 0
for i in range(n):
  x,y = map(int,input().split())
  b.append([x,i])
  b.append([y,i])
  ASUM += x
  BSUM += y
a = sorted(b)
tuka = [0] * n
flag = 0
for i in range(n):
  if tuka[a[i][1]] == 1:
    flag = 1
    break
  else:
    tuka[a[i][1]] = 1
ans = 0
for i in range(n):
  ans += a[i][0]
if flag == 0:
  tmp = float("inf")
  las = a[n-1]
  bu = a[n-2]
  for i in range(n):
    if las[1] == i:
      tmp = min(tmp,max(b[i*2][0],b[i*2+1][0])-bu[0])
    else:
      tmp = min(tmp,max(b[i*2][0],b[i*2+1][0])-las[0])
  ans += tmp
ans = min(ans,ASUM,BSUM)
print(ans)