1133_D. Zero Quantity Maximization
You are given two arrays a and b, each contains n integers.

You want to create a new array c as follows: choose some real (i.e. not necessarily integer) number d, and then for every i ∈ [1, n] let c_i := d ⋅ a_i + b_i.

Your goal is to maximize the number of zeroes in array c. What is the largest possible answer, if you choose d optimally?

Input

The first line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of elements in both arrays.

The second line contains n integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9).

The third line contains n integers b_1, b_2, ..., b_n (-10^9 ≤ b_i ≤ 10^9).

Output

Print one integer — the maximum number of zeroes in array c, if you choose d optimally.

Examples

Input


5
1 2 3 4 5
2 4 7 11 3


Output


2


Input


3
13 37 39
1 2 3


Output


2


Input


4
0 0 0 0
1 2 3 4


Output


0


Input


3
1 2 -1
-6 -12 6


Output


3

Note

In the first example, we may choose d = -2.

In the second example, we may choose d = -1/13.

In the third example, we cannot obtain any zero in array c, no matter which d we choose.

In the fourth example, we may choose d = 6.
```python
from fractions import Fraction

n = int(input())
A = list(map(int, input().split()))
B = list(map(int, input().split()))

count = {}
ans = 0
zeros = 0

for i in range(n):
    if A[i] == 0 and B[i] != 0:
        continue
    elif A[i] == 0 and B[i] == 0:
        zeros += 1
    else:
        temp = Fraction(abs(B[i]), abs(A[i]))
        if A[i] > 0 and B[i] > 0:
            temp *= -1
        elif A[i] < 0 and B[i] < 0:
            temp *= -1

        temp = str(temp)
        if temp not in count:
            count[temp] = 1
        else:
            count[temp] += 1

        ans = max(ans, count[temp])

print(ans + zeros)




# for i in range(n):
#     if A[i] == 0 and B[i] != 0:
#         continue
#     elif A[i] == 0 and B[i] == 0:
#         temp = 0
#     else:
#         temp = Fraction(abs(B[i]), abs(A[i]))
#         if A[i] > 0 and B[i] < 0:
#             pass
#         elif A[i] < 0 and B[i] < 0:
#             temp *= -1
#         elif A[i] > 0 and B[i] > 0:
#             temp *= -1
#         elif A[i] > 0 and B[i] < 0:
#             pass

#     temp = str(temp)

#     if temp not in count:
#         count[temp] = 1
#     else:
#         count[temp] += 1

#     ans = max(ans, count[temp])
```