Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

3
1 5
4 2
6 3

Sample Output 1

7

Consider the cycle 1→3→2→1. The weights of those edges are {\rm min}(A_1,B_3)=1, {\rm min}(A_3,B_2)=2 and {\rm min}(A_2,B_1)=4, for a total of 7.
As there is no cycle with a total weight of less than 7, the answer is 7.

Sample Input 2

4
1 5
2 6
3 7
4 8

Sample Output 2

10

Sample Input 3

6
19 92
64 64
78 48
57 33
73 6
95 73

Sample Output 3

227

Solution in Python (3.4.3) (judge verdict: Time Limit Exceeded)

#! /usr/bin/env python
# -*- coding: utf-8 -*-
# vim:fenc=utf-8
#

"""
AGC028 C
"""

import itertools

n = int(input())
abli0 = [tuple(map(int, input().split())) for i in range(n)]
eabli0 = enumerate(abli0)
abli1 = list(map(lambda t: ((t[1][0], t[0], 0), (t[1][1], t[0], 1)), eabli0))
abli = list(itertools.chain.from_iterable(abli1))
abli.sort(key=lambda t: t[0])
tmpans0 = sum(map(lambda t: t[0], abli[:n]))
alist = []
blist = []
for x, i, aorb in abli[:n]:
    if not aorb:
        alist.append(i)
    else:
        blist.append(i)

flag = False
for i in range(n):
    if i in alist and i in blist:
        flag = True
        break

y, j, arob2 = abli[n]
z, k, arob3 = abli[n+1]
if flag:
    tmpans = tmpans0
else:
    tmpans = 2**62
    for x, i, aorb in abli[:n]:
        if j != i:
            tmp = tmpans0-x+y
        else:
            tmp = tmpans0-x+z
        if tmpans > tmp:
            tmpans = tmp

leftsum = sum(map(lambda x: x[0], abli0))
rightsum = sum(map(lambda x: x[1], abli0))

print(min(leftsum, rightsum, tmpans))