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())
As, Bs = [], []
for i in range(N):
    A, B = map(int, input().split())
    As.append((A, i))
    Bs.append((B, i))

ansA = sum([A for A, i in As])
ansB = sum([B for B, i in Bs])

Cs = sorted(As + Bs)

useds = [False] * N
sumC = 0
for C, i in Cs[:N]:
    useds[i] = True
    sumC += C

if not all(useds):
    ansC = sumC
elif Cs[N-1][1] != Cs[N][1]:
    ansC = sumC - Cs[N-1][0] + Cs[N][0]
else:
    ansC = min(sumC - Cs[N-2][0] + Cs[N][0], sumC - Cs[N-1][0] + Cs[N+1][0])

print(min(ansA, ansB, ansC))
