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 $a_i \lt a_{i+1}$ and $b_i \gt b_{i+1}$ for all $1\le i \lt n$.

To flip a card $i$ means swapping the values of $a_i$ and $b_i$. You must flip some subset of cards (possibly, none), then put all the cards in any order you like. What is the minimum number of cards you must flip in order to sort the deck?

有一副 $n$ 张牌。第 $i$ 张牌正面标有数字 $a_i$，背面标有数字 $b_i$。从 $1$ 到 $2n$ 的每个整数在所有牌上恰好出现一次。

若一副牌满足：所有牌的正面数字严格递增，且所有牌的背面数字严格递减，则称其为已排序的。即对所有 $1 \le i < n$，均有 $a_i \lt a_{i+1}$ 且 $b_i \gt b_{i+1}$。

对第 $i$ 张牌执行翻转操作，是指交换其正面与背面的数值（即交换 $a_i$ 和 $b_i$）。你必须翻转某个子集的牌（该子集可以为空），然后可将所有牌以任意顺序排列。问：为使这副牌变为已排序的，所需的最少翻转次数是多少？

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.

第一行包含一个整数 $n$（$1\le n\le 2\cdot 10^5$）—— 表示卡片的数量。

接下来的 $n$ 行描述这些卡片。其中第 $i$ 行包含两个整数 $a_i, b_i$（$1\le a_i, b_i\le 2n$）。在 $1$ 到 $2n$ 之间的每个整数恰好出现一次。

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

如果无法对牌组进行排序，则输出“-1”。否则，输出对牌组进行排序所需的最少翻转次数。

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 $3 \lt 5 \lt 6 \lt 7 \lt 9$ and $10 \gt 8 \gt 4 \gt 2 \gt 1$.

In the second test case, it is impossible to sort the deck.

在第一个测试用例中，我们翻转卡片 $(1, 9)$ 和 $(2, 7)$。此时牌组变为 $(3,10), (5,8), (6,4), (7,2), (9,1)$。该牌组已排序，因为 $3 \lt 5 \lt 6 \lt 7 \lt 9$ 且 $10 \gt 8 \gt 4 \gt 2 \gt 1$。

在第二个测试用例中，无法将牌组排序。