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.