Problem Statement

There are N trampolines on a two-dimensional planar town where Takahashi lives. The i-th trampoline is located at the point (x_i, y_i) and has a power of P_i. Takahashi's jumping ability is denoted by S. Initially, S=0. Every time Takahashi trains, S increases by 1.
Takahashi can jump from the i-th to the j-th trampoline if and only if:

• $P_iS\geq |x_i - x_j| +|y_i - y_j|$.

Takahashi's objective is to become able to choose a starting trampoline such that he can reach any trampoline from the chosen one with some jumps.
At least how many times does he need to train to achieve his objective?

Input

Input is given from Standard Input in the following format:
N
x_1 y_1 P_1
$\vdots$
x_N y_N P_N

Output

Print the answer.

Constraints

• $2 \leq N \leq 200$
• -$10^9 \leq x_i,y_i \leq 10^9$
• $1 \leq P_i \leq 10^9$
• $(x_i, y_i) \neq (x_j,y_j)$\ $(i\neq j)$
• All values in input are integers.

Sample Input 1

4
-10 0 1
0 0 5
10 0 1
11 0 1

Sample Output 1

2

If he trains twice, S=2,
in which case he can reach any trampoline from the 2-nd one.
For example, he can reach the 4-th trampoline as follows.

• Jump from the 2-nd to the 3-rd trampoline. (Since P_2 S = 10 and |x_2-x_3| + |y_2-y_3| = 10, it holds that $P_2 S \geq |x_2-x_3| + |y_2-y_3|.)$

• Jump from the 3-rd to the 4-th trampoline. (Since P_3 S = 2 and |x_3-x_4| + |y_3-y_4| = 1, it holds that $P_3 S \geq |x_3-x_4| + |y_3-y_4|.)$

Sample Input 2

7
20 31 1
13 4 3
-10 -15 2
34 26 5
-2 39 4
0 -50 1
5 -20 2

Sample Output 2

18

见题面 Input 部分

见题面 Output 部分