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
readline = sys.stdin.readline

N = int(readline())

AB = [tuple(map(int, readline().split())) for _ in range(N)]
A, B = map(list, zip(*AB))

ans = min(sum(A), sum(B))
C = [(A[i], i) for i in range(N)] + [(B[i], i) for i in range(N)]

C.sort()

table = [0]*N
for i in range(N):
    _, idx = C[i]
    table[idx] += 1
if max(table) > 1:
    ans = min(ans, sum(c for (c, _) in C[:N]))

else:
    MAB = list(map(max, AB))
    D = [None]*N
    for i in range(N, 2*N):
        _, idx = C[i]
        D[idx] = i
    
    res = sum(c for (c, _) in C[:N])
    for i in range(N-1):
        _, idx = C[i]
        ans = min(ans, res + MAB[idx] - C[N-1][0])
    ans = min(ans, res + MAB[C[N-1][1]] - C[N-2][0])

print(ans)