Problem: We have an N×N checkerboard.

From the square at the upper left corner, a square that is i squares to the right and j squares below is denoted as (i, j). Particularly, the square at the upper left corner is denoted as (0, 0).

Each square (i, j) such that i+j is even, is colored black, and the other squares are colored white.

We will satisfy the following condition by painting some of the white squares:

* Any black square can be reached from square (0, 0) by repeatedly moving to a black square that shares a side with the current square.



Achieve the objective by painting at most 170000 squares black.

Constraints

* 1 \leq N \leq 1,000

Input

The input is given from Standard Input in the following format:


N


Output

Print the squares to paint in the following format:


K
x_1 y_1
x_2 y_2
:
x_K y_K


This means that a total of K squares are painted black, the i-th of which is (x_i, y_i).

Judging

The output is considered correct only if all of the following conditions are satisfied:

* 0 \leq K \leq 170000
* 0 \leq x_i, y_i \leq N-1
* For each i, x_i + y_i is odd.
* If i \neq j, then (x_i, y_i) \neq (x_j, y_j).
* The condition in the statement is satisfied by painting all specified squares.

Examples

Input

2


Output

1
1 0


Input

4


Output

3
0 1
2 1
2 3

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
using lint = long long int;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template<typename T> istream &operator>>(istream &is, vector<T> &vec){ for (auto &v : vec) is >> v; return is; }
template<typename T> ostream &operator<<(ostream &os, const vector<T> &vec){ os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const deque<T> &vec){ os << "deq["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa){ os << "(" << pa.first << "," << pa.second << ")"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
template<typename T> void ndarray(vector<T> &vec, int len) { vec.resize(len); }
template<typename T, typename... Args> void ndarray(vector<T> &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); }
template<typename T> void Max(T &m, const T q) { if (m < q) m = q; }
template<typename T> void Min(T &m, const T q) { if (m > q) m = q; }
template<typename T1, typename T2> pair<T1, T2> operator+(pair<T1, T2> &l, pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template<typename T1, typename T2> pair<T1, T2> operator-(pair<T1, T2> &l, pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;

int N;

vector<pint> nuru;

struct UnionFind // UnionFind Tree (0-indexed)
{
    vector<int> par, rank;
    UnionFind(int N) : par(N), rank(N) { REP(i, N) par[i] = i; }
    int find(int x) { return (par[x] == x) ? x : (par[x] = find(par[x])); }
    void unite(int x, int y) {
        x = find(x), y = find(y); if (x == y) return;
        if (rank[x] < rank[y]) par[x] = y; else par[y] = x;
        if (rank[x] == rank[y]) rank[x]++;
    }
    bool same(int x, int y) { return find(x) == find(y); }
};

void dfs(int dim, int x, int y)
{
    if (x < 0 || y < 0) return;
    nuru.push_back(pint(x, y));
    if (dim)
    {
        dfs(dim - 1, x, y + (1 << dim));
        dfs(dim - 1, x, y - (1 << dim));
        dfs(dim - 1, x - (1 << dim), y);
        dfs(dim - 1, x + (1 << dim), y);
    }
}

UnionFind uf(1);
void Unite(int x, int y, int N)
{
    int n = x * N + y;
    if (y < N - 1) uf.unite(n, n + 1);
    if (y) uf.unite(n, n - 1);
    if (x) uf.unite(n, n - N);
    if (x < N - 1) uf.unite(n, n + N);
}

int main()
{
    cin >> N;
    int d = 1;
    while((1 << d) < N) d++;
    dfs(d, 0, 1);
    
    vector<pint> nuru_new;
    for (auto pa : nuru) if (pa.first >= 0 and pa.second >= 0 and pa.first < N and pa.second < N) nuru_new.push_back(pa);

    nuru = nuru_new;
    nuru_new.clear();

    uf = UnionFind(N * N);
    for (auto pa : nuru) Unite(pa.first, pa.second, N);

    REP(i, N) REP(j, N) if ((i + j) % 2 == 0)
    {
        int n = i * N + j;
        if (!uf.same(n, 0))
        {
            if (j > 0)
            {
                nuru.push_back(pint(i, j - 1));
                Unite(i, j - 1, N);
            }
            else
            {
                nuru.push_back(pint(i - 1, j));
                Unite(i - 1, j, N);
            }
        }
    }

    printf("%d\n", (int)nuru.size());
    for (auto pa : nuru)
    {
        printf("%d %d\n", pa.first, pa.second);
    }
}