Manao is solving a problem with the following statement:

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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
#include <bits/stdc++.h>
using namespace std;
const int N = 150 * 1001;
int n, m, h, a[N], b[N], seg[N << 2], seg2[N << 2], res;
void build(int s = 0, int e = m, int id = 1) {
  if (e - s == 1) {
    seg[id] = seg2[id] = s - m;
    return;
  }
  int mid = (e + s) >> 1;
  build(s, mid, id * 2);
  build(mid, e, id * 2 + 1);
  seg[id] = min(seg[id * 2], seg[id * 2 + 1]) + seg2[id];
}
void add(int l, int r, int x, int s = 0, int e = m, int id = 1) {
  if (r <= s || e <= l) return;
  if (l <= s && e <= r) {
    seg[id] += x;
    seg2[id] += x;
    return;
  }
  int mid = (e + s) >> 1;
  add(l, r, x, s, mid, id * 2);
  add(l, r, x, mid, e, id * 2 + 1);
  seg[id] = min(seg[id * 2], seg[id * 2 + 1]) + seg2[id];
}
int main() {
  cin >> n >> m >> h;
  for (int i = 0; i < m; i++) {
    cin >> b[i];
    b[i] *= -1;
  }
  sort(b, b + m);
  for (int i = 0; i < n; i++) cin >> a[i];
  build();
  for (int i = 0; i < m; i++) {
    int k = upper_bound(b, b + m, a[i] - h) - b;
    add(0, k, 1);
  }
  if (seg[1] >= 0) res++;
  for (int i = m; i < n; i++) {
    int k = upper_bound(b, b + m, a[i] - h) - b;
    int k2 = upper_bound(b, b + m, a[i - m] - h) - b;
    add(0, k, 1);
    add(0, k2, -1);
    if (seg[1] >= 0) res++;
  }
  cout << res << "\n";
}
