Problem:
Score : 500 points

Problem Statement

There are N integers X_1, X_2, \cdots, X_N, and we know that A_i \leq X_i \leq B_i.
Find the number of different values that the median of X_1, X_2, \cdots, X_N can take.

Notes

The median of X_1, X_2, \cdots, X_N is defined as follows. Let x_1, x_2, \cdots, x_N be the result of sorting X_1, X_2, \cdots, X_N in ascending order.

If N is odd, the median is x_{(N+1)/2};

if N is even, the median is (x_{N/2} + x_{N/2+1}) / 2.

Constraints

2 \leq N \leq 2 \times 10^5

1 \leq A_i \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 answer.

Sample Input 1

2
1 2
2 3

Sample Output 1

3

If X_1 = 1 and X_2 = 2, the median is \frac{3}{2};

if X_1 = 1 and X_2 = 3, the median is 2;

if X_1 = 2 and X_2 = 2, the median is 2;

if X_1 = 2 and X_2 = 3, the median is \frac{5}{2}.

Thus, the median can take three values: \frac{3}{2}, 2, and \frac{5}{2}.

Sample Input 2

3
100 100
10 10000
1 1000000000

Sample Output 2

9991

Solution in Haskell (GHC 8.8.3) (judge verdict: Time Limit Exceeded)

import Data.List
import qualified Data.ByteString.Char8 as BS
import Data.Char

main = do
  li <- BS.getLine
  let Just (n,_) = BS.readInt li
  co <- BS.getContents
  let [as,bs] = transpose $ map (unfoldr (BS.readInt . BS.dropWhile isSpace)) $ BS.lines co
  let ans = compute n as bs
  print ans

-- pureforeverearthのコード
-- https://atcoder.jp/contests/abc169/submissions/13847654
-- をコピーしたもの。これで答えが求まる理屈は理解できていない

compute :: Int -> [Int] -> [Int] -> Int
compute n as bs
  | odd n = b1 - a1 + 1
  | True  = b0 + b1 - a0 - a1 + 1
  where
    a0 = getNth n21 as
    a1 = getNth n2 as
    b0 = getNth n21 bs
    b1 = getNth n2 bs
    n2 = div n 2
    n21 = pred n2

getNth :: Ord a => Int -> [a] -> a
getNth 0 xs = minimum xs
getNth n (x:xs) =
  case compare n k of
    LT -> getNth n as
    EQ -> x
    GT -> getNth (n-k-1) bs
  where
    (as,bs) = partition (x >) xs
    k = length as