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
from operator import itemgetter
from itertools import chain

n = int(input())
aaa = [tuple(map(int, input().split())) for _ in range(n)]
flatten = sorted(chain.from_iterable([(a, i), (b, i)] for i, (a, b) in enumerate(aaa)))
picked = set()
ans = 0

for ab, i in flatten[:n]:
    picked.add(i)
    ans += ab

if len(picked) == n:
    exclude = flatten[n - 1]
    include = flatten[n]
    if exclude[1] == include[1]:
        tmp1 = include[0] - flatten[n - 2][0]
        tmp2 = flatten[n + 1][0] - exclude[0]
        ans += min(tmp1, tmp2)
    else:
        ans -= exclude[0]
        ans += include[0]

ans = min(ans, sum(map(itemgetter(0), aaa)), sum(map(itemgetter(1), aaa)))

print(ans)
