Optimize!

Manao is solving a problem with the following statement:

He came up with a solution that produces the correct answers but is too slow. You are given the pseudocode of his solution, where the function getAnswer calculates the answer to the problem:

getAnswer(a[1..n], b[1..len], h)  
  answer = 0  
  for i = 1 to n-len+1  
    answer = answer + f(a[i..i+len-1], b, h, 1)  
  return answer  
  
f(s[1..len], b[1..len], h, index)  
  if index = len+1 then  
    return 1  
  for i = 1 to len  
    if s[index] + b[i] >= h  
      mem = b[i]  
      b[i] = 0  
      res = f(s, b, h, index + 1)  
      b[i] = mem  
      if res > 0  
        return 1  
  return 0  

Your task is to help Manao optimize his algorithm.

Input

The first line contains space-separated integers n, len and h (1 ≤ len ≤ n ≤ 150000; 1 ≤ h ≤ 109). The second line contains len space-separated integers b1, b2, ..., blen (1 ≤ bi ≤ 109). The third line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 109).

Output

Print a single number — the answer to Manao's problem.

Examples

Input

5 2 10 5 3 1 8 5 5 7

Output

2

inputFormat

Input

The first line contains space-separated integers n, len and h (1 ≤ len ≤ n ≤ 150000; 1 ≤ h ≤ 109). The second line contains len space-separated integers b1, b2, ..., blen (1 ≤ bi ≤ 109). The third line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 109).

outputFormat

Output

Print a single number — the answer to Manao's problem.

Examples

Input

5 2 10 5 3 1 8 5 5 7

Output

2

样例

5 2 10
5 3
1 8 5 5 7

2

</p>