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

from collections import deque
import itertools as it
import sys
import math

sys.setrecursionlimit(1000000)

INF = 10 ** 18
MOD = 10 ** 9 + 7

N = input()
ls = []
A_ = []
B_ = []
for i in range(N):
    A, B = map(int, raw_input().split())
    A_.append(A)
    B_.append(B)
    ls.append((A, 'A', i))
    ls.append((B, 'B', i))

ls.sort()

used = [[False] * N, [False] * N]

S = 0
for i in range(N):
    p = ls[i]
    S += p[0]
    if p[1] == 'A':
        used[0][p[2]] = True
    else:
        used[1][p[2]] = True

if True in used[0] and True in used[1]:
    pass
else:
    print S
    exit()

for i in range(N):
    if used[0][i] and used[1][i]:
        print S
        exit()

ans = INF
for i in range(N):
    T = S
    pos = N
    if ls[pos][2] == i:
        pos += 1
    if used[0][i]:
        T -= A_[i]
        T += ls[pos][0]
    else:
        T -= B_[i]
        T += ls[pos][0]
    ans = min(ans, T)

print ans