Score : $1500$ points

Problem Statement

You have $N$ sets $S_1, S_2, \ldots, S_N$. Initially, for each $i$ from $1$ to $N$, set $S_i$ contains only integer $i$ (that is, $S_i = \{i\}$).

You are allowed to perform the following operation:

• Choose any $i$ with $1 \le i \le N-1$. Let $U = S_i \cup S_{i+1}$ ー the union of sets $S_i$ and $S_{i+1}$. Then, replace both $S_i$ and $S_{i+1}$ with $U$.

You want to perform a finite number of operations above (maybe zero), to get a configuration, in which $S_i = \{L_i, L_i+1, \ldots, R_i-1, R_i\}$ for all $i$ from $1$ to $N$. Is it possible to reach this configuration? If it is possible, also find the smallest number of operations needed to reach it.

Constraints

• $1 \le N \le 5\cdot 10^5$
• $1 \le L_i \le R_i \le N$

Input

Input is given from Standard Input in the following format:

$N$

$L_1$ $R_1$

$L_2$ $R_2$

$\vdots$

$L_N$ $R_N$

Output

If it is possible to reach the required configuration, output the smallest number of operations needed to do it. Otherwise, output -1.

3
1 2
1 2
1 3

-1

It can be proved that it's impossible to obtain the required configuration.

4
1 3
1 4
1 4
2 4

4

We can perform the following sequence of operations:

• Choose $i = 2$, get $S_1 = \{1\}, S_2 = \{2, 3\}, S_3 = \{2, 3\}, S_4 = \{4\}$
• Choose $i = 1$, get $S_1 = \{1, 2, 3\}, S_2 = \{1, 2, 3\}, S_3 = \{2, 3\}, S_4 = \{4\}$
• Choose $i = 3$, get $S_1 = \{1, 2, 3\}, S_2 = \{1, 2, 3\}, S_3 = \{2, 3, 4\}, S_4 = \{2, 3, 4\}$
• Choose $i = 2$, get $S_1 = \{1, 2, 3\}, S_2 = \{1, 2, 3, 4\}, S_3 = \{1, 2, 3, 4\}, S_4 = \{2, 3, 4\}$