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
import sys
input = sys.stdin.readline

n=int(input())
A=[]

A1=0
B1=0

for i in range(n):
    a,b=map(int,input().split())
    
    A1+=a
    B1+=b
    
    A.append((a,2*i))
    A.append((b,2*i+1))


ANS=min(A1,B1)

A.sort()
INVIND=[-1]*(2*n)

for ind,(a,i) in enumerate(A):
    INVIND[i]=ind

S=[0]

for a,i in A:
    S.append(S[-1]+a)


for i in range(n):
    if INVIND[i*2]<n and INVIND[i*2+1]<n:
        ANS=min(ANS,S[n])

    elif INVIND[i*2]<n-1 and INVIND[i*2+1]>=n-1:
        ANS=min(ANS,A[INVIND[i*2+1]][0]+S[n-1])

    elif INVIND[i*2]>=n-1 and INVIND[i*2+1]<n-1:
        ANS=min(ANS,A[INVIND[i*2]][0]+S[n-1])

    else:
        ANS=min(ANS,S[n-2]+A[INVIND[i*2]][0]+A[INVIND[i*2+1]][0])

    #print(i,ANS)

print(ANS)
