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
N = int(sys.stdin.buffer.readline())
AB = list(map(int, sys.stdin.buffer.read().split()))
A = AB[::2]
B = AB[1::2]
ans = min(sum(A), sum(B))
AB.sort()
pivot = AB[N-1]
pivot2 = AB[N]
pivot_idxs = []
pivot2_idxs = []
ans2 = sum(AB[:N])
for i, (a, b) in enumerate(zip(A, B)):
    if a <= pivot and b <= pivot:
        ans = min(ans, ans2)
        print(ans)
        exit()
    if a == pivot or b == pivot:
        pivot_idxs.append(i)
    if a == pivot2 or b == pivot2:
        pivot2_idxs.append(i)

if len(pivot_idxs) == len(pivot2_idxs) == 1 and pivot_idxs[0] == pivot2_idxs[0]:
    ans2 = min(
        ans2 - pivot + AB[N+1],
        ans2 - AB[N-2] + pivot2
    )
else:
    ans2 = ans2 - pivot + pivot2
ans = min(ans, ans2)
print(ans)
