p03233 AtCoder Grand Contest 028 - Min Cost Cycle
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
```python
import sys
import socket

if socket.gethostname() in ['N551J', 'F551C']:
    test_case = 'c1.in'
    sys.stdin = open(test_case)


def read_int_list():
    return list(map(int, input().split()))


def read_int():
    return int(input())


def read_str_list():
    return input().split()


def read_str():
    return input()


def solve():
    n = read_int()
    rows = [read_int_list() for i in range(n)]
    a, b = map(list, zip(*rows))
    res = sum(a)
    res = min(res, sum(b))
    all_values = [(a[i], i, 0) for i in range(n)]
    all_values.extend([(b[i], i, 1) for i in range(n)])
    all_values.sort()
    index_of_value = {v: i for i, v in enumerate(all_values)}
    first_values = [
        set(all_values[:n - 2]),
        set(all_values[:n - 1]),
        set(all_values[:n]),
    ]

    s = [sum([t[0] for t in v]) for v in first_values]
    for i in range(n):
        rest = []
        k = 0
        last = n - 2
        indices = sorted([(index_of_value[(a[i], i, 0)], a[i]),
                          (index_of_value[(b[i], i, 1)], b[i])])

        for index, value in indices:
            if index < last:
                last += 1
                k += 1
            else:
                rest.append(value)
        t = s[k] + sum(rest)
        res = min(res, t)
    return res


def main():
    res = solve()
    print(res)


if __name__ == '__main__':
    main()

```