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.

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.

Constraints

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

Sample Input 1

3
1 2
1 2
1 3

Sample Output 1

-1

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

Sample Input 2

4
1 3
1 4
1 4
2 4

Sample Output 2

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}

见题面 Input 部分

见题面 Output 部分