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=[]
node=[]
for i in range(N):
  x,y=map(int,input().split())
  A.append((x,i,"left"))
  A.append((y,i,"right"))
  node.append((x,y))
  
A.sort()
Used=[[False,False] for i in range(N)]
Used_node=0
for i in range(N):
  if A[i][2]=="left":
    Used[A[i][1]][0]=True
    if not Used[A[i][1]][1]:
      Used_node+=1
  if A[i][2]=="right":
    Used[A[i][1]][1]=True
    if not Used[A[i][1]][0]:
      Used_node+=1
if Used_node!=N:
  ans=0
  for i in range(N):
    ans+=A[i][0]
  print(ans)
else:
  if Used[0][0]:
    f=0
  else:
    f=1
  NO=0
  for i in range(N):
    if not Used[i][f]:
      NO=1
      break
  ans=0
  for i in range(N):
    ans+=A[i][0]
  ans2=float("inf")
  if NO==1:
    for w in range(N):
      if A[N][1]==w:
        ans2=min(ans2,ans-min(node[w])+A[N+1][0])
      else:
        ans2=min(ans2,ans-min(node[w])+A[N][0])
    print(ans2)
    exit()
  print(ans)
    