There are
N parts of some source code. The characteristics of the
ith part of the code are represented by
M integers
Ai1,
Ai2< /sub>,
...,
AiM . You are given integers
B1,
B2,
...< /font>, BM , and C.
The ith part of the code solves the problem correctly if and only if \( A_{i1}\cdot B_1 + A_{i2} \cdot B_2 + ...+ A_{iM}\cdot B_M +C>0\).
Among the N parts of the source code, find the number that correctly solve this problem.
Input
The first line contains three space-separated numbers: N, M (1 <= N, M <= 20) and C (- 100 <= C <= 100). The second line contains M numbers Bi (-100 <= Bi <= 100). Each of the following N lines contains M numbers Ai (-100 <= A ij <= 100, 1 <= i <= N, 1 <= j <= M).
Imprint
Print one number - the answer to the problem.
Examples
| # |
Input |
Output |
| 1 |
2 3 -10
1 2 3
3 2 1
1 2 2
| 1 |
| 2 |
5 2 -4
-2 5
100 41
100 40
-3 0
-6 -2
18-13 |
2 |
| 3 |
3 3 0
100 -100 0
0 100 100
100 100 100
-100 100 100
| 0 |