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 Python (3.4.3) (judge verdict: Runtime Error)

import sys
sys.setrecursionlimit(10000000)
def input():
    return sys.stdin.readline()[:-1]
from bisect import *
from collections import *
from heapq import *
from math import *
from itertools import *

def abc103():
    N = int(input())
    U, V = [None] * N, [None] * N
    OK = True
    for i in range(N):
        x, y = map(int, input().split())
        u, v = x+y, x-y
        U[i], V[i] = u, v
        if i != 0:
            if f ^ (u%2):
                OK = False
        f = u%2
    if OK == False:
        print(-1)
        exit()
    D = [2**i for i in range(30, -1, -1)] + [1]*f
    print(31-f)
    print(*D)
    for u, v in zip(U, V):
        ans = []
        pu, pv = 0, 0
        for d in D:
            if pu <= u and pv <= v:
                pu += d
                pv += d
                ans.append('R')
            elif pu <= u and pv >= v:
                pu += d
                pv -= d
                ans.append('U')
            elif pu >= u and pv >= v:
                pu -= d
                pv -= d
                ans.append('L')
            elif pu >= u and pv <= v:
                pu -= d
                pv += d
                ans.append('U')
        print(*ans, sep = '')

abc103()