Problem:
Score : 300 points

Problem Statement

A sequence a_1,a_2,... ,a_n is said to be /\/\/\/ when the following conditions are satisfied:

For each i = 1,2,..., n-2, a_i = a_{i+2}.

Exactly two different numbers appear in the sequence.

You are given a sequence v_1,v_2,...,v_n whose length is even.
We would like to make this sequence /\/\/\/ by replacing some of its elements.
Find the minimum number of elements that needs to be replaced.

Constraints

2 \leq n \leq 10^5

n is even.

1 \leq v_i \leq 10^5

v_i is an integer.

Input

Input is given from Standard Input in the following format:

n
v_1 v_2 ... v_n

Output

Print the minimum number of elements that needs to be replaced.

Sample Input 1

4
3 1 3 2

Sample Output 1

1

The sequence 3,1,3,2 is not /\/\/\/, but we can make it /\/\/\/ by replacing one of its elements: for example, replace the fourth element to make it 3,1,3,1.

Sample Input 2

6
105 119 105 119 105 119

Sample Output 2

0

The sequence 105,119,105,119,105,119 is /\/\/\/.

Sample Input 3

4
1 1 1 1

Sample Output 3

2

The elements of the sequence 1,1,1,1 are all the same, so it is not /\/\/\/.

Solution in C (GCC 5.4.1) (judge verdict: Accepted)


#include <stdio.h>
#include <stdlib.h>

struct number{
    int s;
    int num;
};

int dsc(const void *a, const void *b){
    struct number *A = (struct number *)a;
    struct number *B = (struct number *)b;
    return B->s - A->s;
}

int minimum(int a, int b){ return a < b ? a : b; }

int main(){
    int n, v[100000], i, temp;
    int cnt0, cnt1;
    struct number even[100001], odd[100001];

    scanf("%d", &n);
    for(i=0; i<100001; i++){
        even[i].s = 0;
        even[i].num = i;
        odd[i].s = 0;
        odd[i].num = i;
    }
    for(i=0; i<n; i++){
        if(i%2==0){
            scanf("%d", &temp);
            odd[temp].s++;
            v[i] = temp;
        }
        else{
            scanf("%d", &temp);
            even[temp].s++;
            v[i] = temp;
        }
    }

    qsort(even, 100001, sizeof(struct number), dsc);
    qsort(odd, 100001, sizeof(struct number), dsc);

    if(even[0].num == odd[0].num){
        cnt0=0; cnt1=0;
        for(i=0; i<n; i++){
            if(i%2==0){
                if(v[i] != odd[0].num)
                    cnt0++;
                
                if(v[i] != odd[1].num)
                    cnt1++;
            }
            else{
                if(v[i] != even[1].num)
                    cnt0++;

                if(v[i] != even[0].num)
                    cnt1++;
            }
        }
        printf("%d\n", minimum(cnt0, cnt1));
    }
    else{
        cnt0=0;
        for(i=0; i<n; i++){
            if(i%2==0){
                if(v[i] != odd[0].num)
                    cnt0++;
            }
            else{
                if(v[i] != even[0].num)
                    cnt0++;
            }
        }
        printf("%d\n", cnt0);
    }

    return 0;
}