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 = []
for i in range(N):
    a, b = map(int, input().split())
    A += [a]
    B += [b]
s1 = sum(A)
s2 = sum(B)
C = A + B
C.sort()
s3 = sum(C[:N])
s4 = sum(C[N:])
check = 1
m1 = C[N-1]
m2 = C[N-2]
for i in range(N):
    a = min(A[i], B[i])
    b = max(A[i], B[i])
    if b < m1:
        check = 0
        break
    elif b == m1 and a != b:
        check = 0
        break
    elif a < m1:
        s4 = min(s4, s3 - m1 + b)
    elif a == m1:
        s4 = min(s4, s3 - m2 + b)
if check == 0:
    print(min(s1, s2, s3))
else:
    print(min(s1, s2, s4))