VU atrankinis turas 2005 m. ACM ICPC varžyboms

Vova invited all his friends to his birthday party. After the apple pie had been eaten and juice had been drunk, the children decided to play the Green Darts game. The rules of the game are quite simple:

• N players take part in the game (1 ≤ N ≤ 100);
• each player throws a dart into a target 3 times, with each throw bringing from 0 to 100 points;
• the final score of player i is calculated by the formula

S_i = a_i1∙p² + a_i2∙p + a_i3,

• where S_i is the final score of the player i; a_ij is the number of points from the throw j of player i (integer, 0 ≤ a_ij ≤ 100); and p is some coefficient (real number, 0 < p ≤ 1).

After the calculation of all S_i we can determine the rank M_i of the player i by the formula M_i = K_i + 1, where K_i is the number of players whose the final score is greater than S_i.

We can see that several players could have the same rank. Finally, we can form the game result as the vector (M₁, M₂, …, M_N). Two game results are different if the corresponding vectors don't coincide. Vova's friends decide to offer him the choice of the coefficient p. Vova would like to know whether his choice could affect the result of the game. He doesn't know the answer to the following question: how many different results of the game exist, depending on the choice of the coefficient p? Help Vova to solve this hard problem!

Input

The first line of input file contains integer number N. Each of the following N lines contains 3 integer numbers a_i1, a_i2, a_i3, separated by single spaces - the number of points which the 1st, 2nd and 3rd throw brought to player the player i.

Output

The first and only line of the output file should contain the number of different game results.

Sample Input

3
1 99 1
100 100 100
51 49 13

Sample Output

3