Problem: After you had helped George and Alex to move in the dorm, they went to help their friend Fedor play a new computer game «Call of Soldiers 3».

The game has (m + 1) players and n types of soldiers in total. Players «Call of Soldiers 3» are numbered form 1 to (m + 1). Types of soldiers are numbered from 0 to n - 1. Each player has an army. Army of the i-th player can be described by non-negative integer xi. Consider binary representation of xi: if the j-th bit of number xi equal to one, then the army of the i-th player has soldiers of the j-th type. 

Fedor is the (m + 1)-th player of the game. He assume that two players can become friends if their armies differ in at most k types of soldiers (in other words, binary representations of the corresponding numbers differ in at most k bits). Help Fedor and count how many players can become his friends.

Input

The first line contains three integers n, m, k (1 ≤ k ≤ n ≤ 20; 1 ≤ m ≤ 1000).

The i-th of the next (m + 1) lines contains a single integer xi (1 ≤ xi ≤ 2n - 1), that describes the i-th player's army. We remind you that Fedor is the (m + 1)-th player.

Output

Print a single integer — the number of Fedor's potential friends.

Examples

Input

7 3 1
8
5
111
17


Output

0


Input

3 3 3
1
2
3
4


Output

3

Solution (in PYTHON3):

Solution:
def convert_base(num, t=2, f=10):
    if f != 10:
        num = int(str(num), f)
    alphabet = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
    if num < t:
        return alphabet[num]
    else:
        return convert_base(num // t, t) + alphabet[num % t]


n, m, k = map(int, input().split())
a = sorted([convert_base(int(input())).zfill(n) for _ in range(m)])

x = convert_base(int(input())).zfill(n)

ans = 0

for p in a:
    diff = 0
    for i in range(n):
        if p[i] != x[i]:
            diff += 1
    if diff <= k:
        ans += 1

print(ans)