Problem:
Score : 700 points

Problem Statement

You are given an integer L. Construct a directed graph that satisfies the conditions below. The graph may contain multiple edges between the same pair of vertices. It can be proved that such a graph always exists.

The number of vertices, N, is at most 20. The vertices are given ID numbers from 1 to N.

The number of edges, M, is at most 60. Each edge has an integer length between 0 and 10^6 (inclusive).

Every edge is directed from the vertex with the smaller ID to the vertex with the larger ID. That is, 1,2,...,N is one possible topological order of the vertices.

There are exactly L different paths from Vertex 1 to Vertex N. The lengths of these paths are all different, and they are integers between 0 and L-1.

Here, the length of a path is the sum of the lengths of the edges contained in that path, and two paths are considered different when the sets of the edges contained in those paths are different.

Constraints

2 \leq L \leq 10^6

L is an integer.

Input

Input is given from Standard Input in the following format:

L

Output

In the first line, print N and M, the number of the vertices and edges in your graph.
In the i-th of the following M lines, print three integers u_i,v_i and w_i, representing the starting vertex, the ending vertex and the length of the i-th edge.
If there are multiple solutions, any of them will be accepted.

Sample Input 1

4

Sample Output 1

8 10
1 2 0
2 3 0
3 4 0
1 5 0
2 6 0
3 7 0
4 8 0
5 6 1
6 7 1
7 8 1

In the graph represented by the sample output, there are four paths from Vertex 1 to N=8:

1 → 2 → 3 → 4 → 8 with length 0

1 → 2 → 3 → 7 → 8 with length 1

1 → 2 → 6 → 7 → 8 with length 2

1 → 5 → 6 → 7 → 8 with length 3

There are other possible solutions.

Sample Input 2

5

Sample Output 2

5 7
1 2 0
2 3 1
3 4 0
4 5 0
2 4 0
1 3 3
3 5 1

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

/*
 * じょえチャンネル
 * 高評価・チャンネル登録よろしくおねがいします！
 * https://www.youtube.com/channel/UCRXsI3FL_kvaVL9zoolBfbQ
 */

#include <bits/stdc++.h>

//#pragma GCC target("avx2")
//#pragma GCC optimize("O3")
//#pragma GCC optimize("unroll-loops")

#define f(i,n) for(int i=0;i<(n);i++)




//here!!!
// define int long long !!!!!

#define int long long

// define int long long !!!!!


#define mod (int)((1e9)+7)
//constexpr int mod = 998244353ll;


#ifdef int
#define inf (int)(3e18)
#else
#define inf (int)(5e8)
#endif

#define intt long long
#define itn long long
#define P pair<long long,long long>

#define rep(i,n) for(int i=0;i<n;i++)
#define REP(i,n) for(int i=1;i<=n;i++)

#define ALL(v) v.begin(),v.end()

using namespace std;

//Library
//モッドパウ
inline int modpow(int x, int y, int m = mod) {
    int res = 1;
    while (y) {
        if (y & 1) {
            res *= x;
            res %= m;
        }
        x = x * x % m;
        y /= 2;
    }
    return res;
}

int mypow(int x, int y) {
    int res = 1;
    while (y) {
        if (y % 2) {
            res *= x;
        }
        x = x * x;
        y /= 2;
    }
    return res;
}
//is the number (x) a prime number?
bool prime(int x) {
    for (int i = 2; i * i <= x; i++) {
        if (!(x % i)) {
            return false;
        }
    }
    return true;
}


//saidai-kouyakusuu
inline int gcd(int x, int y) {
    if (!y) {
        return x;
    }
    return gcd(y, x % y);
}


//number of keta
int keta(int x) {
    int ans = 0;
    while (x) {
        x /= 10;
        ans++;
    }
    return ans;
}

//sum of keta
int ketasum(int x) {
    int ans = 0;
    while (x) {
        ans += x % 10;
        x /= 10;
    }
    return ans;
}

inline int lcm(int x, int y) {
    int ans = x / gcd(x, y) * y;
    return ans;
}
int twobeki(int x) {
    int ans = 0;
    while (1) {
        if (!(x & 1)) {
            ans++;
            x /= 2;
        }
        else {
            break;
        }
    }
    return ans;
}


template <class T, class U>
inline bool chmax(T& lhs, const U& rhs) {
    if (lhs < rhs) {
        lhs = rhs;
        return 1;
    }
    return 0;
}
template <class T, class U>
inline bool chmin(T& lhs, const U& rhs) {
    if (lhs > rhs) {
        lhs = rhs;
        return 1;
    }
    return 0;
}
void Yes(){
    cout<<"Yes"<<endl;
}
void No(){
    cout<<"No"<<endl;
}
void YES(){
    cout<<"YES"<<endl;
}
void NO(){
    cout<<"NO"<<endl;
}


#define fin(i) scanf("%lld",&i)
#define fout(i) printf("%lld",i)
#define fendl printf("\n")

int kai(int x, int y) {
    int res = 1;
    for (int i = x - y + 1; i <= x; i++) {
        res *= i; res %= mod;
    }
    return res;
}

int comb(int x, int y) {
    if (y > x)return 0;
    //    cout<<kai(x, y)<<' '<<modpow(kai(y, y), mod - 2)<<endl;
    return kai(x, y) * modpow(kai(y, y), mod - 2) % mod;
}
//Library-End


#define vecin(v) for(int i=0;i<v.size();i++)scanf("%lld",&v[i]);
#define vecout(v) {for(int i=0;i<(int)v.size();i++)printf("%lld ",v[i]);printf("\n");}


template<typename T, typename U>
class SegTree {
protected:
    unsigned int n = 1, rank = 0;
    std::vector<T> node;
    T nodee;
    virtual T nodef(const T&, const T&)const = 0;
public:
    SegTree(unsigned int m, T init, T nodee):nodee(nodee) {
        while (n < m) {
            n *= 2;
            rank++;
        }
        node.resize(2 * n);
        for (unsigned int i = n; i < 2 * n; i++)node[i] = init;
    }
    SegTree(const std::vector<T>& initvec, T nodee):nodee(nodee) {
        unsigned int m = initvec.size();
        while (n < m) {
            n *= 2;
            rank++;
        }
        node.resize(2 * n);
        for (unsigned int i = n; i < 2 * n; i++) {
            if (i - n < m)node[i] = initvec[i - n];
        }
    }
    virtual void update(int i, U x) {
        i += n;
        node[i] = x;
        while (i != 1) {
            i >>= 1;
            node[i] = nodef(node[2 * i], node[2 * i + 1]);
        }
    }
    virtual T query(int l, int r) {
        l += n; r += n;
        int ls = nodee, rs = nodee;
        while (l < r) {
            if (l & 1) {
                ls = nodef(ls, node[l]);
                l++;
            }
            if (r & 1) {
                r--;
                rs = nodef(node[r], rs);
            }
            l >>= 1; r >>= 1;
        }
        return nodef(ls, rs);
    }
    virtual T operator[](const int& x) {
        return node[n + x];
    }
    void fill(T x) {
        std::fill(all(node), x);
    }
    void print() {
        rep(i, n)std::cout << operator[](i) << " ";
        std::cout << std::endl;
    }
};
class RSQ :public SegTree<int, int> {
    int nodef(const int& lhs,const int& rhs){return lhs+rhs;}
public:
    RSQ(int size, const int& def = 0) :SegTree<int, int>(size, def, 0) {}
    RSQ(const std::vector<int>& initvec) :SegTree<int, int>(initvec, 0) {}
};
class RMiQ :public SegTree<int, int> {
    int nodef(const int& lhs,const int& rhs){return std::min(lhs,rhs);}
public:
    RMiQ(int size, const int& def = 0) :SegTree<int, int>(size, def, 0) {}
    RMiQ(const std::vector<int>& initvec) :SegTree<int, int>(initvec, 0) {}
};
class RMaQ :public SegTree<int, int> {
    int nodef(const int& lhs,const int& rhs){return std::max(lhs,rhs);}
public:
    RMaQ(int size, const int& def = 0) :SegTree<int, int>(size, def, 0) {}
    RMaQ(const std::vector<int>& initvec) :SegTree<int, int>(initvec, 0) {}
};
template<typename T, typename U>
class IntervalSegTree :public SegTree<T, U> {
protected:
    using SegTree<T, U>::n;
    using SegTree<T, U>::rank;
    using SegTree<T, U>::node;
    using SegTree<T, U>::nodef;
    using SegTree<T, U>::nodee;
    std::vector<U> lazy;
    std::vector<bool> lazyflag;
    std::vector<int> width;
    virtual void lazyf(U&, const U&) = 0;
    virtual void updf(T&, const U&, const unsigned int&) = 0;
    void eval(int k) {
        for (int i = rank; i > 0; i--) {
            int nk = k >> i;
            if (lazyflag[nk]) {
                updf(node[2 * nk], lazy[nk], width[2 * nk]);
                updf(node[2 * nk + 1], lazy[nk], width[2 * nk + 1]);
                if (lazyflag[2 * nk])lazyf(lazy[2 * nk], lazy[nk]);
                else lazy[2 * nk] = lazy[nk];
                if (lazyflag[2 * nk + 1])lazyf(lazy[2 * nk + 1], lazy[nk]);
                else lazy[2 * nk + 1] = lazy[nk];
                lazyflag[2 * nk] = lazyflag[2 * nk + 1] = true;
                lazyflag[nk] = false;
            }
        }
    }
public:
    IntervalSegTree(unsigned int m, T init, T nodee) :SegTree<T, U>(m, init, nodee) {
        lazy.resize(2 * n); lazyflag.resize(2 * n); width.resize(2 * n);
        width[1] = n;
        for (unsigned int i = 2; i < 2 * n; i++) {
            width[i] = width[i >> 1] >> 1;
        }
    }
    IntervalSegTree(T nodee, const std::vector<T>& initvec) :SegTree<T, U>(initvec, nodee) {
        lazy.resize(2 * n); lazyflag.resize(2 * n); width.resize(2 * n);
        width[1] = n;
        for (unsigned int i = 2; i < 2 * n; i++) {
            width[i] = width[i >> 1] >> 1;
        }
    }
    void update(int i, U x) {
        i += n;
        eval(i);
        updf(node[i], x, width[i]);
        if (lazyflag[i])lazyf(lazy[i], x);
        else {
            lazyflag[i] = true;
            lazy[i] = x;
        }
        while (i /= 2)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
    void update(int l, int r, U x) {
        l += n; r += n;
        int nl = l, nr = r;
        while (!(nl & 1))nl >>= 1;
        while (!(nr & 1))nr >>= 1;
        nr--;
        eval(nl); eval(nr);
        while (l < r) {
            if (l & 1) {
                updf(node[l], x, width[l]);
                if (lazyflag[l])lazyf(lazy[l], x);
                else {
                    lazyflag[l] = true;
                    lazy[l] = x;
                }
                l++;
            }
            if (r & 1) {
                r--;
                updf(node[r], x, width[r]);
                if (lazyflag[r])lazyf(lazy[r], x);
                else {
                    lazyflag[r] = true;
                    lazy[r] = x;
                }
            }
            l >>= 1; r >>= 1;
        }
        while (nl >>= 1)node[nl] = nodef(node[2 * nl], node[2 * nl + 1]);
        while (nr >>= 1)node[nr] = nodef(node[2 * nr], node[2 * nr + 1]);
    }
    T query(int l, int r) {
        l += n; r += n;
        eval(l); eval(r - 1);
        int ls = nodee, rs = nodee;
        while (l < r) {
            if (l & 1) {
                ls = nodef(ls, node[l]);
                l++;
            }
            if (r & 1) {
                r--;
                rs = nodef(node[r], rs);
            }
            l >>= 1; r >>= 1;
        }
        return nodef(ls, rs);
    }
    T operator[](const int& x) {
        eval(n + x);
        return node[n + x];
    }
    T queryForAll() {
        return node[1];
    }
};
class RAQRSQ :public IntervalSegTree<int, int> {
    int nodef(const int& a, const int& b)const { return a + b; }
    void lazyf(int& a, const int& b) { a += b; }
    void updf(int& a, const int& b, const unsigned int& width) { a += width * b; }
public:
    RAQRSQ(int size, const int& def = 0) :IntervalSegTree<int, int>(size, def, 0) {
        for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
    RAQRSQ(const std::vector<int>& initvec) :IntervalSegTree<int, int>((int)0, initvec) {
        for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
};
class RAQRMiQ :public IntervalSegTree<int, int> {
    int nodef(const int& a, const int& b)const { return std::min(a, b); }
    void lazyf(int& a, const int& b) { a += b; }
    void updf(int& a, const int& b, const unsigned int& width) { a += b; }
public:
    RAQRMiQ(int size, const int& def = 0) :IntervalSegTree<int, int>(size, def, inf) {
        for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
    RAQRMiQ(const std::vector<int>& initvec) :IntervalSegTree<int, int>(inf, initvec) {
        for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
};
class RAQRMaQ :public IntervalSegTree<int, int> {
    int nodef(const int& a, const int& b)const { return std::max(a, b); }
    void lazyf(int& a, const int& b) { a += b; }
    void updf(int& a, const int& b, const unsigned int& width) { a += b; }
public:
    RAQRMaQ(unsigned int size, const int& def = 0) :IntervalSegTree<int, int>(size, def, -inf) {
        for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
    RAQRMaQ(const std::vector<int>& initvec) :IntervalSegTree<int, int>(-inf, initvec) {
        for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
};
class RUQRSQ :public IntervalSegTree<int, int> {
    int nodef(const int& a, const int& b)const { return a + b; }
    void lazyf(int& a, const int& b) { a = b; }
    void updf(int& a, const int& b, const unsigned int& width) { a = width * b; }
public:
    RUQRSQ(int size, const int& def = 0) :IntervalSegTree<int, int>(size, def, 0) {
        for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
    RUQRSQ(const std::vector<int>& initvec) :IntervalSegTree<int, int>((int)0, initvec) {
        for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
};
class RUQRMiQ :public IntervalSegTree<int, int> {
    int nodef(const int& a, const int& b)const { return std::min(a, b); }
    void lazyf(int& a, const int& b) { a = b; }
    void updf(int& a, const int& b, const unsigned int& width) { a = b; }
public:
    RUQRMiQ(int size, const int& def = 0) :IntervalSegTree<int, int>(size, def, inf) {
        for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
    RUQRMiQ(const std::vector<int>& initvec) :IntervalSegTree<int, int>(inf, initvec) {
        for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
};
class RUQRMaQ :public IntervalSegTree<int, int> {
    int nodef(const int& a, const int& b)const { return std::max(a, b); }
    void lazyf(int& a, const int& b) { a = b; }
    void updf(int& a, const int& b, const unsigned int& width) { a = b; }
public:
    RUQRMaQ(int size, const int& def = 0) :IntervalSegTree<int, int>(size, def, -inf) {
        for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
    RUQRMaQ(const std::vector<int>& initvec) :IntervalSegTree<int, int>(-inf, initvec) {
        for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
};

#define R_MIN ([](long long a, long long b) { return min(a, b); })
#define R_MAX ([](long long a, long long b) { return max(a, b); })
#define R_SUM ([](long long a, long long b) { return a + b; })

#define NORMAL_UPDATE ([](long long a, long long b) { return b; })
#define ADD_UPDATE ([](long long a, long long b) { return a + b; })
#define MINUS_UPDATE ([](long long a, long long b) { return a - b; }

class Union_Find {
    vector<int> par;
    vector<int> rankmy;
    vector<int> ookisa;
    
public:
    Union_Find(int size) {
        par = vector<int>(size);
        rankmy = vector<int>(size);
        ookisa=vector<int>(size);
        for (int i = 0; i < size; i++) {
            par[i] = i;
            ookisa[i]=1;
        }
    }
    
    int find(int x) {
        if (par[x] == x) {
            return x;
        }
        return par[x] = find(par[x]);
    }
    
    void unite(int x, int y) {
        x = find(x);
        y = find(y);
        if (x == y) {
            return;
        }
        if (rankmy[x] < rankmy[y]) {
            par[x] = y;
            ookisa[y]+=ookisa[x];
            ookisa[x]=0;
        }
        else {
            par[y] = x;
            ookisa[x]+=ookisa[y];
            ookisa[y]=0;
            if (rankmy[x] == rankmy[y]) {
                rankmy[x]++;
            }
        }
    }
    int size(int i){
        i=find(i);
        return ookisa[i];
    }
    bool same(int x, int y){
        return find(x) == find(y);
    }
    
};

//Union-Find-End

int perm[1000005];
void init_perm() {
    perm[0] = 1;
    REP(i, 1000000) {
        perm[i] = perm[i - 1] * i % mod;
    }
}

int nCk(int x, int y) {
    return perm[x] * modpow(perm[x - y], mod - 2) % mod * modpow(perm[y], mod - 2) % mod;
}

double kyori(pair<int, int> f, pair<int, int> s) {
    double ans = 0;
    double t = fabs(f.first - s.first);
    double y = fabs(f.second - s.second);
    ans = sqrt(t * t + y * y);
    return ans;
}

inline string stringmax(string& x,string& y){
    if (x.size()>y.size()) {
        return x;
    }
    if (x.size()<y.size()) {
        return y;
    }
    rep(i,x.size()){
        if (x[i]>y[i]) {
            return x;
        }
        if (x[i]<y[i]) {
            return y;
        }
    }
    return x;
}

#define endl "\n" //interactive の時に注意！！！
#define printd cout<<fixed<<setprecision(10)

int l,cnt,now,n;
vector<pair<P, int>> v;
signed main(){
    ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    cin>>l;
    
    now=1;
    while (now<=l) {
        now*=2;
        cnt++;
    }
    now=1;
    cnt--;
    n=cnt+1;
    l--;
    REP(i,cnt){
        v.push_back({{i,i+1},0});
        v.push_back({{i,i+1},now});
        now*=2;
    }
    now=(1ll<<cnt);
    while (now<=l) {
        int ta=1;
        int c=0;
        while (now+ta-1<=l) {
            ta*=2;
            c++;
        }
        c--;
        ta/=2;
        v.push_back({{c+1,n},now});
        now+=ta+1;
    }
    cout<<n<<' '<<v.size()<<endl;
    rep(i,v.size()){
        cout<<v[i].first.first<<' '<<v[i].first.second<<' '<<v[i].second<<endl;
    }
}