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



Sample input:
3
1 5
4 2
6 3


Sample output:
7

Submission status: Runtime Error

Solution code:
n = int(input())
li= []
for i in range(n):
    li.append(list(map(int,input().split())))
a1 = list(itertools.permutations(range(n)))
min1 = float('inf')
for i in a1:
    if i[n-1] != 0:
        continue
    listi = list(i)
    listi.insert(0,0)
    aa = 0
    for j in range(len(listi)-1):
        aa += min(li[listi[j]][0],li[listi[j+1]][1])
    if aa < min1:
        min1 = aa
print(min1)