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 = []
Sa = 0
Sb = 0
for i in range(N):
    a,b = map(int,input().split())
    A.append([a,i])
    B.append([b,i])
    Sa += a
    Sb += b
C = sorted(A+B)
ind = []
ans = 0
for i in range(N):
    ind.append(C[i][1])
    ans += C[i][0]
ind = set(ind)
if len(ind) == N:
    if C[N-1][1] != C[N][1]:
        ans += C[N][0]-C[N-1][0]
    else:
        ans += min(C[N][0]-C[N-2][0],C[N+1][0]-C[N-1][0])
ans = min(Sa,Sb,ans)
print(ans)