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 maxn = 150000 + 15;
struct Node {
  int minn, delt;
  Node() { minn = delt = 0; }
} tree[maxn * 4];
int n, len, upp;
int b[maxn], a[maxn], f[maxn];
int found(int x) {
  int l = 0, r = len + 1, midd;
  while (l + 1 < r) {
    midd = (l + r) >> 1;
    if (x + b[midd] >= upp)
      r = midd;
    else
      l = midd;
  }
  return r;
}
int up(int root) {
  tree[root].minn = min(tree[root << 1].minn, tree[root << 1 | 1].minn);
  return 0;
}
int down(int root) {
  if (tree[root].delt == 0) return 0;
  int delt = tree[root].delt;
  tree[root].delt = 0;
  tree[root << 1].minn += delt;
  tree[root << 1].delt += delt;
  tree[root << 1 | 1].minn += delt;
  tree[root << 1 | 1].delt += delt;
  return 0;
}
int build(int root, int l, int r) {
  if (l == r) {
    tree[root].minn = -l;
    return 0;
  }
  int mid = (l + r) >> 1;
  build(root << 1, l, mid);
  build(root << 1 | 1, mid + 1, r);
  up(root);
  return 0;
}
int inser(int root, int l, int r, int x, int y, int z) {
  if (x > r || y < l) return 0;
  if (x <= l && r <= y) {
    tree[root].minn += z;
    tree[root].delt += z;
    return 0;
  }
  down(root);
  int mid = (l + r) >> 1;
  inser(root << 1, l, mid, x, y, z);
  inser(root << 1 | 1, mid + 1, r, x, y, z);
  up(root);
  return 0;
}
int main() {
  scanf("%d%d%d", &n, &len, &upp);
  for (int i = 1; i <= len; i++) scanf("%d", &b[i]);
  sort(b + 1, b + len + 1);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    f[i] = found(a[i]);
  }
  build(1, 1, len);
  for (int i = 1; i < len; i++)
    if (f[i] <= len) inser(1, 1, len, f[i], len, 1);
  int sum = 0;
  for (int i = 0; i <= n - len; i++) {
    if (i != 0) {
      if (f[i] <= len) inser(1, 1, len, f[i], len, -1);
    }
    if (f[i + len] <= len) inser(1, 1, len, f[i + len], len, 1);
    if (tree[1].minn >= 0) sum++;
  }
  printf("%d\n", sum);
  return 0;
}
