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())

edge = []
num_list = []

for i in range(n):
    a, b = map(int, input().split())
    edge.append([a, b])
    num_list.append(a)
    num_list.append(b)

num_list.sort()
K = num_list[n-1]

ab = []
ax = []
xb = []

for i in range(n):
    a, b = edge[i]
    if a <= K and b <= K:
        ab.append(edge[i])
    elif a <= K:
        ax.append(edge[i])
    elif b <= K:
        xb.append(edge[i])

if len(ab) > 0:
    ans = sum(num_list[:n])
elif len(ax) == n or len(xb) == n:
    ans = sum(num_list[:n])
else:
    yabai_edge = num_list[n-1:n+1]
    if edge.count(yabai_edge) + edge.count(yabai_edge[::-1]) == 0:
        diff = num_list[n] - num_list[n-1]
    elif len(ax) == 1 and edge.count(yabai_edge) == 1:
        diff = num_list[n] - num_list[n-1]
    elif len(xb) == 1 and edge.count(yabai_edge[::-1]) == 1:
        diff = num_list[n] - num_list[n-1]
    else:
        diff = min(num_list[n+1]-num_list[n-1], num_list[n]-num_list[n-2]) 
    ans = sum(num_list[:n]) + diff

print(ans)


