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 sys import exit, setrecursionlimit, stderr
from functools import reduce
from itertools import *
from collections import defaultdict, Counter
from bisect import bisect

def read():
  return int(input())

def reads():
  return [int(x) for x in input().split()]

N = read()
A = [0] * N; B = [0] * N
for i in range(N):
  A[i], B[i] = reads()

ans = 10 ** 18
ans = min(ans, sum(A))
ans = min(ans, sum(B))

s = sorted([(A[i], i) for i in range(N)] + [(B[i], i) for i in range(N)])

used = [False] * N
for i in range(N):
  used[s[i][1]] = True
cand = sum(a for a, i in s[:N])
if not all(used):
  ans = min(ans, cand)
else:
  if s[N-1][1] != s[N][1]:
    ans = min(ans, cand - s[N-1][0] + s[N][0])
  else:
    ans = min(ans, cand - s[N-2][0] + s[N][0])
    ans = min(ans, cand - s[N-1][0] + s[N+1][0])
print(ans)
