CF1503D Flip the Cards

There is a deck of $ n $ cards. The $ i $ -th card has a number $ a_i $ on the front and a number $ b_i $ on the back. Every integer between $ 1 $ and $ 2n $ appears exactly once on the cards. A deck is called sorted if the front values are in increasing order and the back values are in decreasing order. That is, if $ a_i< a_{i+1} $ and $ b_i> b_{i+1} $ for all $ 1\le i

The first line contains a single integer $ n $ ( $ 1\le n\le 2\cdot 10^5 $ ) — the number of cards. The next $ n $ lines describe the cards. The $ i $ -th of these lines contains two integers $ a_i, b_i $ ( $ 1\le a_i, b_i\le 2n $ ). Every integer between $ 1 $ and $ 2n $ appears exactly once.

If it is impossible to sort the deck, output "-1". Otherwise, output the minimum number of flips required to sort the deck.

In the first test case, we flip the cards $ (1, 9) $ and $ (2, 7) $ . The deck is then ordered $ (3,10), (5,8), (6,4), (7,2), (9,1) $ . It is sorted because $ 31 $ . In the second test case, it is impossible to sort the deck.