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())
D = []
for i in range(N):
    a, b = map(int, input().split())
    D.append((a, 0, i))
    D.append((b, 1, i))

D.sort()
ans = 0
C = [False] * N
db = False
gr = [0] * 2
for i in range(N):
    ans += D[i][0]
    gr[D[i][1]] += 1
    if C[D[i][2]]:
        db = True
    C[D[i][2]] = True

if not db and gr[0] != 0 and gr[1] != 0:
    if D[N - 1][2] == D[N][2]:
        ans = min(ans - D[N - 2][0] + D[N][0], ans - D[N - 1][0] + D[N + 1][0])
    else:
        ans = ans - D[N - 1][0] + D[N][0]

print(ans)