Problem Statement

Takahashi wants to buy the popular video game console called Play Snuke. There are $N$ shops that sell Play Snuke: Shop $1, 2, \dots, N$. Shop $i$ is $A_i$ minutes' walk from where Takahashi is now, sells Play Snuke for $P_i$ yen (Japanese currency), and currently has $X_i$ Play Snukes in stock. Now, Takahashi will go to one of those shops on foot and buy Play Snuke if it is still in stock when he gets there. However, Play Snuke is so popular that the number of consoles in stock (if any) in every shop will decrease by $1$ at the following moments: $0.5, 1.5, 2.5, \dots$ minutes from now. Determine whether Takahashi can buy Play Snuke. If he can, find the minimum amount of money needed to buy one.

Constraints

• All values in input are integers.
• $1 ≤ N ≤ 10^5$
• $1 ≤ A_i, P_i, X_i ≤ 10^9$

Input

Input is given from Standard Input in the following format:

N
A_1 P_1 X_1
\vdots
A_N P_N X_N

Output

If Takahashi can buy Play Snuke, print the minimum amount of money needed to buy one, as an integer. If he cannot buy one, print -1.