#include <bits/stdc++.h>
using namespace std;
#pragma comment(linker, "/stack:200000000")
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
template <typename T>
bool mmax(T &m, const T q) {
  if (m < q) {
    m = q;
    return true;
  } else
    return false;
}
template <typename T>
bool mmin(T &m, const T q) {
  if (m > q) {
    m = q;
    return true;
  } else
    return false;
}
void __print(long long first) { cerr << first; }
void __print(long first) { cerr << first; }
void __print(unsigned first) { cerr << first; }
void __print(unsigned long first) { cerr << first; }
void __print(unsigned long long first) { cerr << first; }
void __print(float first) { cerr << first; }
void __print(double first) { cerr << first; }
void __print(long double first) { cerr << first; }
void __print(char first) { cerr << '\'' << first << '\''; }
void __print(const char *first) { cerr << '\"' << first << '\"'; }
void __print(const string &first) { cerr << '\"' << first << '\"'; }
void __print(bool first) { cerr << (first ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V> &first) {
  cerr << '{';
  __print(first.first);
  cerr << ',';
  __print(first.second);
  cerr << '}';
}
template <typename T>
void __print(const T &first) {
  long long f = 0;
  cerr << '{';
  for (auto &i : first) cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
long long dx[] = {0, 0, 1, -1};
long long dy[] = {1, -1, 0, 0};
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long n, s, l;
  cin >> n >> s >> l;
  vector<long long> a(n);
  for (long long i = 0; i < n; i++) cin >> a[i];
  if (l > n) {
    cout << -1 << endl;
    return 0;
  }
  vector<long long> res(n + 1, 2e9);
  res[0] = 0;
  multiset<long long> L;
  multiset<long long> value;
  long long t = 0;
  for (long long i = 0; i < l - 1; i++) value.insert(a[i]);
  for (long long i = l - 1; i < n; i++) {
    L.insert(res[i - l + 1]);
    value.insert(a[i]);
    while (L.size() && (*(value.rbegin()) - (*(value.begin())) > s)) {
      L.erase(L.find(res[t]));
      value.erase(value.find(a[t]));
      t++;
    }
    if (L.size()) res[i + 1] = 1 + *(L.begin());
  }
  if (res[n] >= 2e9) res[n] = -1;
  cout << res[n] << endl;
  return 0;
}

### Prompt

Your challenge is to write a CPP solution to the following problem:

Alexandra has a paper strip with n numbers on it. Let's call them ai from left to right.

Now Alexandra wants to split it into some pieces (possibly 1). For each piece of strip, it must satisfy:

  * Each piece should contain at least l numbers.
  * The difference between the maximal and the minimal number on the piece should be at most s.



Please help Alexandra to find the minimal number of pieces meeting the condition above.

Input

The first line contains three space-separated integers n, s, l (1 ≤ n ≤ 105, 0 ≤ s ≤ 109, 1 ≤ l ≤ 105).

The second line contains n integers ai separated by spaces ( - 109 ≤ ai ≤ 109).

Output

Output the minimal number of strip pieces.

If there are no ways to split the strip, output -1.

Examples

Input

7 2 2
1 3 1 2 4 1 2


Output

3


Input

7 2 2
1 100 1 100 1 100 1


Output

-1

Note

For the first sample, we can split the strip into 3 pieces: [1, 3, 1], [2, 4], [1, 2].

For the second sample, we can't let 1 and 100 be on the same piece, so no solution exists.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
#pragma comment(linker, "/stack:200000000")
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
template <typename T>
bool mmax(T &m, const T q) {
  if (m < q) {
    m = q;
    return true;
  } else
    return false;
}
template <typename T>
bool mmin(T &m, const T q) {
  if (m > q) {
    m = q;
    return true;
  } else
    return false;
}
void __print(long long first) { cerr << first; }
void __print(long first) { cerr << first; }
void __print(unsigned first) { cerr << first; }
void __print(unsigned long first) { cerr << first; }
void __print(unsigned long long first) { cerr << first; }
void __print(float first) { cerr << first; }
void __print(double first) { cerr << first; }
void __print(long double first) { cerr << first; }
void __print(char first) { cerr << '\'' << first << '\''; }
void __print(const char *first) { cerr << '\"' << first << '\"'; }
void __print(const string &first) { cerr << '\"' << first << '\"'; }
void __print(bool first) { cerr << (first ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V> &first) {
  cerr << '{';
  __print(first.first);
  cerr << ',';
  __print(first.second);
  cerr << '}';
}
template <typename T>
void __print(const T &first) {
  long long f = 0;
  cerr << '{';
  for (auto &i : first) cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
long long dx[] = {0, 0, 1, -1};
long long dy[] = {1, -1, 0, 0};
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long n, s, l;
  cin >> n >> s >> l;
  vector<long long> a(n);
  for (long long i = 0; i < n; i++) cin >> a[i];
  if (l > n) {
    cout << -1 << endl;
    return 0;
  }
  vector<long long> res(n + 1, 2e9);
  res[0] = 0;
  multiset<long long> L;
  multiset<long long> value;
  long long t = 0;
  for (long long i = 0; i < l - 1; i++) value.insert(a[i]);
  for (long long i = l - 1; i < n; i++) {
    L.insert(res[i - l + 1]);
    value.insert(a[i]);
    while (L.size() && (*(value.rbegin()) - (*(value.begin())) > s)) {
      L.erase(L.find(res[t]));
      value.erase(value.find(a[t]));
      t++;
    }
    if (L.size()) res[i + 1] = 1 + *(L.begin());
  }
  if (res[n] >= 2e9) res[n] = -1;
  cout << res[n] << endl;
  return 0;
}

```