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

"""
AGC028 C
"""

from operator import itemgetter

n = int(input())
abli = []
for i in range(n):
    a, b = map(int, input().split())
    abli.append((a, i, 0))
    abli.append((b, i, 1))

abli.sort(key=itemgetter(0))
tmpans0 = sum(map(itemgetter(0), abli[:n]))
aiset = set([i for x, i, aorb in abli[:n] if not aorb])
biset = set([i for x, i, aorb in abli[:n] if aorb])
flag = bool(set.intersection(aiset, biset))


y, j, arob2 = abli[n]
z, k, arob3 = abli[n+1]

if flag:
    tmpans = tmpans0
else:
    min1 = y-max([x for x, i, aorb in abli[:n] if j != i])
    min2 = z-max([x for x, i, aorb in abli[:n] if j == i])
    tmpans = tmpans0 + min(min1, min2)

leftsum = sum([aa for aa, i, aorb in abli if not aorb])
rightsum = sum([bb for bb, i, aorb in abli if aorb])

print(min(leftsum, rightsum, tmpans))
