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;
inline int in() {
  int x;
  scanf("%d", &x);
  return x;
}
const int N = 1e6 + 10;
const int MOD = 1e9 + 7;
const long double eps = 1e-12;
int seg[4 * N], n, len, h, a[N], b[N], lazy[4 * N];
void shift(int idx) {
  lazy[idx * 2 + 0] += lazy[idx];
  lazy[idx * 2 + 1] += lazy[idx];
  seg[idx * 2 + 0] += lazy[idx];
  seg[idx * 2 + 1] += lazy[idx];
  lazy[idx] = 0;
}
void update(int ql, int qr, int val, int l = 0, int r = len, int idx = 1) {
  if (qr <= l || r <= ql) return;
  if (ql <= l && r <= qr) {
    lazy[idx] += val;
    seg[idx] += val;
    return;
  }
  shift(idx);
  int mid = (l + r) / 2;
  update(ql, qr, val, l, mid, idx * 2 + 0);
  update(ql, qr, val, mid, r, idx * 2 + 1);
  seg[idx] = min(seg[idx * 2 + 0], seg[idx * 2 + 1]);
}
int main() {
  n = in();
  len = in();
  h = in();
  for (int i = 0; i < len; i++) b[i] = in();
  for (int i = 0; i < n; i++) a[i] = in();
  sort(b, b + len);
  for (int i = 0; i < n; i++) a[i] = int(lower_bound(b, b + len, h - a[i]) - b);
  for (int i = 0; i < len; i++) update(i, i + 1, -i - 1);
  for (int i = 0; i < len - 1; i++) update(a[i], len, +1);
  int ans = 0;
  for (int i = len - 1; i < n; i++) {
    update(a[i], len, +1);
    if (seg[1] >= 0) ans++;
    update(a[i - len + 1], len, -1);
  }
  cout << ans;
  return 0;
}
