#include <bits/stdc++.h>
using namespace std;
template <typename T>
void read(T &x) {
  cin >> x;
}
template <typename T, typename T0>
void read(T &x, T0 &y) {
  cin >> x >> y;
}
template <typename T, typename T0, typename T1>
void read(T &x, T0 &y, T1 &z) {
  cin >> x >> y >> z;
}
template <typename T, typename T0, typename T1, typename T2>
void read(T &x, T0 &y, T1 &z, T2 &w) {
  cin >> x >> y >> z >> w;
}
template <typename T, typename T0>
void read(pair<T, T0> &p) {
  cin >> p.fst >> p.scd;
}
template <typename T>
void read(vector<T> &oneD) {
  for (long long int i = 0; i < (int)(oneD).size(); i++) {
    read(oneD[i]);
  }
}
template <typename T>
void read(T oneD[], long long int n) {
  for (long long int i = 0; i < n; i++) {
    read(oneD[i]);
  }
}
template <typename T>
void write(T &x) {
  cout << x << " ";
}
template <typename T, typename T0>
void write(T &x, T0 &y) {
  cout << x << " " << y << "\n";
}
template <typename T, typename T0, typename T1>
void write(T &x, T0 &y, T1 &z) {
  cout << x << " " << y << " " << z << "\n";
}
template <typename T, typename T0, typename T1, typename T2>
void write(T &x, T0 &y, T1 &z, T2 &w) {
  cout << x << " " << y << " " << z << " " << w << "\n";
}
template <typename T, typename T0>
void write(pair<T, T0> &p) {
  write(p.fst);
  write(p.scd);
  cout << endl;
}
template <typename T>
void write(vector<T> &oneD) {
  for (long long int i = 0; i < (int)(oneD).size(); i++) {
    write(oneD[i]);
  }
  cout << endl;
}
template <typename T>
void write(T oneD[], int n) {
  for (long long int i = 0; i < n; i++) {
    write(oneD[i]);
  }
  cout << endl;
}
template <typename T, typename T0>
void write(map<T, T0> &mpp) {
  for (auto it : mpp) {
    write(it.fst);
    cout << ": ";
    write(it.scd);
    cout << "\n";
  }
  cout << endl;
}
template <typename T>
inline bool umax(T &x, T y) {
  return (y > x) ? x = y, true : false;
}
template <typename T>
inline bool umin(T &x, T y) {
  return (y < x) ? x = y, true : false;
}
template <class T>
void offset(long long int o, T &x) {
  x += o;
}
template <class T>
void offset(long long int o, vector<T> &x) {
  for (auto &a : x) offset(o, a);
}
template <class T, size_t S>
void offset(long long int o, array<T, S> &x) {
  for (auto &a : x) offset(o, a);
}
inline bool isSquare(long long int x) {
  long long int s = sqrt(x);
  return (s * s == x);
}
inline bool isPowerOfTwo(long long int x) {
  return ((1LL << (long long int)log2(x)) == x);
}
long long int extended_GCD(long long int a, long long int b, long long int &x,
                           long long int &y) {
  if (a == 0) {
    x = 0;
    y = 1;
    return b;
  }
  long long int x1, y1;
  long long int gcd = extended_GCD(b % a, a, x1, y1);
  x = y1 - (b / a) * x1;
  y = x1;
  return gcd;
}
vector<long long int> prime;
void sieve(long long int N) {
  bool isPrime[N + !1];
  for (long long int i = 0; i <= N; ++i) {
    isPrime[i] = true;
  }
  isPrime[0] = false;
  isPrime[1] = false;
  for (long long int i = 2; i * i <= N; ++i) {
    if (isPrime[i] == true) {
      for (long long int j = i * i; j <= N; j += i) isPrime[j] = false;
    }
  }
  for (long long int i = 2; i <= N; i++) {
    if (isPrime[i] == true) {
      prime.push_back(i);
    }
  }
}
long long int minPrime[(int)(1 * 1e6 + 10)];
void factorSieve(long long int n) {
  memset(minPrime, 0, sizeof(minPrime));
  for (long long int i = 2; i * i <= n; ++i) {
    if (minPrime[i] == 0) {
      for (long long int j = i * i; j <= n; j += i) {
        if (minPrime[j] == 0) {
          minPrime[j] = i;
        }
      }
    }
  }
  for (long long int i = 2; i <= n; ++i) {
    if (minPrime[i] == 0) {
      minPrime[i] = i;
    }
  }
}
long long int factorize(long long int n) {
  map<long long int, long long int> m;
  m.clear();
  while (n != 1) {
    m[minPrime[n]]++;
    n /= minPrime[n];
  }
  for (auto i : m) {
    if (i.second > 1) {
      return 0;
    }
  }
  return 1;
}
string to_string(char c) { return string(1, c); }
void solve() {
  long long int n, b;
  read(n);
  b = n;
  long long int a = (n + 2) / 2;
  cout << a;
  cout << "\n";
  for (long long int i = (0); ((1) > 0 ? i < (a) : i > (a)); i += (1)) {
    if (b) {
      cout << 1 << " " << i + 1;
      cout << "\n";
      b--;
    }
  }
  for (long long int i = (1); ((1) > 0 ? i < (a) : i > (a)); i += (1)) {
    if (b) {
      cout << i + 1 << " " << a;
      cout << "\n";
      b--;
    }
  }
}
int main() {
  int t = 1;
  for (long long int i = (0); ((1) > 0 ? i < (t) : i > (t)); i += (1)) {
    solve();
  }
}

### Prompt

Please create a solution in CPP to the following problem:

Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <typename T>
void read(T &x) {
  cin >> x;
}
template <typename T, typename T0>
void read(T &x, T0 &y) {
  cin >> x >> y;
}
template <typename T, typename T0, typename T1>
void read(T &x, T0 &y, T1 &z) {
  cin >> x >> y >> z;
}
template <typename T, typename T0, typename T1, typename T2>
void read(T &x, T0 &y, T1 &z, T2 &w) {
  cin >> x >> y >> z >> w;
}
template <typename T, typename T0>
void read(pair<T, T0> &p) {
  cin >> p.fst >> p.scd;
}
template <typename T>
void read(vector<T> &oneD) {
  for (long long int i = 0; i < (int)(oneD).size(); i++) {
    read(oneD[i]);
  }
}
template <typename T>
void read(T oneD[], long long int n) {
  for (long long int i = 0; i < n; i++) {
    read(oneD[i]);
  }
}
template <typename T>
void write(T &x) {
  cout << x << " ";
}
template <typename T, typename T0>
void write(T &x, T0 &y) {
  cout << x << " " << y << "\n";
}
template <typename T, typename T0, typename T1>
void write(T &x, T0 &y, T1 &z) {
  cout << x << " " << y << " " << z << "\n";
}
template <typename T, typename T0, typename T1, typename T2>
void write(T &x, T0 &y, T1 &z, T2 &w) {
  cout << x << " " << y << " " << z << " " << w << "\n";
}
template <typename T, typename T0>
void write(pair<T, T0> &p) {
  write(p.fst);
  write(p.scd);
  cout << endl;
}
template <typename T>
void write(vector<T> &oneD) {
  for (long long int i = 0; i < (int)(oneD).size(); i++) {
    write(oneD[i]);
  }
  cout << endl;
}
template <typename T>
void write(T oneD[], int n) {
  for (long long int i = 0; i < n; i++) {
    write(oneD[i]);
  }
  cout << endl;
}
template <typename T, typename T0>
void write(map<T, T0> &mpp) {
  for (auto it : mpp) {
    write(it.fst);
    cout << ": ";
    write(it.scd);
    cout << "\n";
  }
  cout << endl;
}
template <typename T>
inline bool umax(T &x, T y) {
  return (y > x) ? x = y, true : false;
}
template <typename T>
inline bool umin(T &x, T y) {
  return (y < x) ? x = y, true : false;
}
template <class T>
void offset(long long int o, T &x) {
  x += o;
}
template <class T>
void offset(long long int o, vector<T> &x) {
  for (auto &a : x) offset(o, a);
}
template <class T, size_t S>
void offset(long long int o, array<T, S> &x) {
  for (auto &a : x) offset(o, a);
}
inline bool isSquare(long long int x) {
  long long int s = sqrt(x);
  return (s * s == x);
}
inline bool isPowerOfTwo(long long int x) {
  return ((1LL << (long long int)log2(x)) == x);
}
long long int extended_GCD(long long int a, long long int b, long long int &x,
                           long long int &y) {
  if (a == 0) {
    x = 0;
    y = 1;
    return b;
  }
  long long int x1, y1;
  long long int gcd = extended_GCD(b % a, a, x1, y1);
  x = y1 - (b / a) * x1;
  y = x1;
  return gcd;
}
vector<long long int> prime;
void sieve(long long int N) {
  bool isPrime[N + !1];
  for (long long int i = 0; i <= N; ++i) {
    isPrime[i] = true;
  }
  isPrime[0] = false;
  isPrime[1] = false;
  for (long long int i = 2; i * i <= N; ++i) {
    if (isPrime[i] == true) {
      for (long long int j = i * i; j <= N; j += i) isPrime[j] = false;
    }
  }
  for (long long int i = 2; i <= N; i++) {
    if (isPrime[i] == true) {
      prime.push_back(i);
    }
  }
}
long long int minPrime[(int)(1 * 1e6 + 10)];
void factorSieve(long long int n) {
  memset(minPrime, 0, sizeof(minPrime));
  for (long long int i = 2; i * i <= n; ++i) {
    if (minPrime[i] == 0) {
      for (long long int j = i * i; j <= n; j += i) {
        if (minPrime[j] == 0) {
          minPrime[j] = i;
        }
      }
    }
  }
  for (long long int i = 2; i <= n; ++i) {
    if (minPrime[i] == 0) {
      minPrime[i] = i;
    }
  }
}
long long int factorize(long long int n) {
  map<long long int, long long int> m;
  m.clear();
  while (n != 1) {
    m[minPrime[n]]++;
    n /= minPrime[n];
  }
  for (auto i : m) {
    if (i.second > 1) {
      return 0;
    }
  }
  return 1;
}
string to_string(char c) { return string(1, c); }
void solve() {
  long long int n, b;
  read(n);
  b = n;
  long long int a = (n + 2) / 2;
  cout << a;
  cout << "\n";
  for (long long int i = (0); ((1) > 0 ? i < (a) : i > (a)); i += (1)) {
    if (b) {
      cout << 1 << " " << i + 1;
      cout << "\n";
      b--;
    }
  }
  for (long long int i = (1); ((1) > 0 ? i < (a) : i > (a)); i += (1)) {
    if (b) {
      cout << i + 1 << " " << a;
      cout << "\n";
      b--;
    }
  }
}
int main() {
  int t = 1;
  for (long long int i = (0); ((1) > 0 ? i < (t) : i > (t)); i += (1)) {
    solve();
  }
}

```