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 Rust (1.15.1) (judge verdict: Accepted)

#[allow(unused_imports)] use std::cmp::{max, min, Ordering};
#[allow(unused_imports)] use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)] use std::iter::FromIterator;
use std::io::Write;
static mut GLOBAL_STDIN: *mut std::io::Stdin = 0usize as _;
static mut GLOBAL_STDINLOCK: *mut std::io::StdinLock<'static> = 0usize as _;
static mut GLOBAL_STDOUT: *mut std::io::Stdout = 0usize as _;
static mut GLOBAL_STDOUTLOCK: *mut std::io::StdoutLock<'static> = 0usize as _;
const BUF_SIZE: usize = 1024*1024;
static mut GLOBAL_INPUT_BUF: *mut u8 = 0usize as _;
static mut GLOBAL_INPUT_PTR: *const u8 = 0usize as _;
static mut GLOBAL_INPUT_END: *const u8 = 0usize as _;
fn init() {
    unsafe {
        use std::boxed::Box;
        GLOBAL_STDIN = Box::into_raw(Box::new(std::io::stdin()));
        GLOBAL_STDINLOCK = Box::into_raw(Box::new(GLOBAL_STDIN.as_ref().unwrap().lock()));
        GLOBAL_STDOUT = Box::into_raw(Box::new(std::io::stdout()));
        GLOBAL_STDOUTLOCK = Box::into_raw(Box::new(GLOBAL_STDOUT.as_mut().unwrap().lock()));
        let buf = Box::<[u8]>::into_raw(vec![0u8; BUF_SIZE].into_boxed_slice());
        GLOBAL_INPUT_BUF = (*buf).as_mut_ptr();
        GLOBAL_INPUT_PTR = GLOBAL_INPUT_BUF;
        GLOBAL_INPUT_END = GLOBAL_INPUT_BUF;
    }
}
fn peek() -> u8 { unsafe {
    use std::io::Read;
    if GLOBAL_INPUT_PTR == GLOBAL_INPUT_END {
        let n = GLOBAL_STDINLOCK.as_mut().unwrap().read(std::slice::from_raw_parts_mut(GLOBAL_INPUT_BUF, BUF_SIZE)).expect("I/O error");
        GLOBAL_INPUT_PTR = GLOBAL_INPUT_BUF;
        GLOBAL_INPUT_END = GLOBAL_INPUT_PTR.offset(n as isize);
    }
    *GLOBAL_INPUT_PTR
} }
fn getchar() -> u8 { let c = peek(); unsafe { GLOBAL_INPUT_PTR = GLOBAL_INPUT_PTR.offset(1); } c }
fn ungetc() { unsafe { GLOBAL_INPUT_PTR = GLOBAL_INPUT_PTR.offset(-1); } }
fn skip_whitespaces() { loop { match getchar() as char { ' ' | '\t' | '\n' | '\r' => { }, _ => { ungetc(); break; } } } }
trait FastRead { fn read() -> Self; }
macro_rules! read_int_impl {
    ( $signed:expr, $($T:ident,)* ) => {
        $(impl FastRead for $T {
            fn read() -> $T {
                skip_whitespaces(); let is_negative = if $signed && peek() == '-' as u8 { getchar(); true } else { false }; let mut val: $T = 0;
                loop {
                    let c = getchar(); let d = c.wrapping_sub('0' as u8);
                    if d >= 10 { match c as char {
                        ' ' | '\t' | '\n' | '\r' => { ungetc(); return if is_negative { 0-val } else { val }; },
                        _ => panic!("invalid input character: `{}' (code: {})", c as char, c),
                    }}
                    val = 10*val + (d as $T);
                }
            }
        })*
    };
}
macro_rules! read_tuple_impl {
    ( ) => ();
    ( $a:ident, $($name:ident,)* ) => {
        impl<$a:FastRead, $($name:FastRead),*> FastRead for ($a, $($name,)*) { fn read() -> Self { ( $a::read(), $($name::read()),* ) } }
        read_tuple_impl!($($name,)*);
    }
}
macro_rules! snd_arg_impl { ($a:expr; $e:expr) => { $e }; }
macro_rules! read_array_impl {
    () => {};
    ($len:expr, $($lens:expr,)*) => {
        impl <T: FastRead> FastRead for [T; $len] { fn read() -> Self { [ $(snd_arg_impl!($lens; read::<T>())),* ] } }
        read_array_impl!($($lens,)*);
    };
}
unsafe fn extend_vec(v: &mut Vec<u8>, first: *const u8, last: *const u8) {
    let len = usize::wrapping_sub(last as _, first as _);
    v.extend_from_slice(&std::slice::from_raw_parts(first, len));
}
macro_rules! read_string_inplace {
    ($func:ident, $($pattern:pat)|+) => {
        #[allow(unused)] fn $func(s: &mut String) -> bool {
            skip_whitespaces();
            unsafe { let mut ptr = GLOBAL_INPUT_PTR; let end = GLOBAL_INPUT_END; let v = s.as_mut_vec(); v.clear();
                     loop {
                         if ptr == end { extend_vec(v, GLOBAL_INPUT_PTR, end); GLOBAL_INPUT_PTR = GLOBAL_INPUT_END; peek(); ptr = GLOBAL_INPUT_PTR; }
                         match *ptr as char {
                             $($pattern)|+ => { extend_vec(v, GLOBAL_INPUT_PTR, ptr); GLOBAL_INPUT_PTR = ptr; return v.is_empty(); }
                             _ => { ptr = ptr.offset(1); }
                         }
                     }
            }
        }
    };
}
read_string_inplace!(getword, ' ' | '\t' | '\n' | '\r');
read_string_inplace!(getline, '\n');
#[allow(unused)] fn read_line() -> String { let mut s = String::new(); getline(&mut s); s }
impl FastRead for String { fn read() -> String { let mut s = String::new(); getword(&mut s); s } }
impl FastRead for char { fn read() -> char { skip_whitespaces(); getchar() as char } }
read_int_impl!(false, u8, u16, u32, u64, usize,);
read_int_impl!(true,  i8, i16, i32, i64, isize,);
read_tuple_impl!(T1, T2, T3, T4, T5, T6, T7, T8, T9, T10, T11, T12,);
read_array_impl!(12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0,);
#[allow(dead_code)] fn read<T: FastRead>() -> T { T::read() }
#[allow(unused_macros)] macro_rules! print   { ($($arg:tt)*) => { write!  (unsafe { GLOBAL_STDOUTLOCK.as_mut().unwrap() }, $($arg)*).unwrap() } }
#[allow(unused_macros)] macro_rules! println { ($($arg:tt)*) => { writeln!(unsafe { GLOBAL_STDOUTLOCK.as_mut().unwrap() }, $($arg)*).unwrap() } }
#[allow(dead_code)] fn read_vec<T: FastRead>(n: usize) -> Vec<T> { let mut v = Vec::with_capacity(n); for _ in 0..n { v.push(read()); } v }
#[allow(dead_code)] fn print_iter<I: Iterator<Item=T>, T: std::fmt::Display>(iter: I) { let mut iter = iter; if let Some(x) = iter.next() { print!("{}", x); for x in iter { print!(" {}", x); } } println!(""); }
#[allow(dead_code)] fn print_vec<T: std::fmt::Display>(v: &Vec<T>) { print_iter(v.iter()); }
#[allow(unused_macros)] macro_rules! debug { ($a:expr, $($b:expr),*) => (if cfg!(debug_assertions) { println!(concat!("DEBUG: ", stringify!($a), " = {:?}", $(", ", stringify!($b), " = {:?}"),*), $a, $($b),*); } ) }
//================================================================================

fn main() {
    init();
    let mut l: u64 = read();
    let mut edges: Vec<(usize, usize, u64)> = Vec::new();
    let mut cnt = Vec::new();
    cnt.push(1);
    edges.push((0, 1, 0));
    edges.push((0, 1, 1));
    edges.push((0, 1, 2));
    cnt.push(3);
    edges.push((1, 2, 0));
    edges.push((1, 2, 3));
    edges.push((1, 2, 6));
    cnt.push(9);
    for i in 2..18 {
        let bak = *cnt.last().unwrap();
        edges.push((i, i+1, 0));
        edges.push((i, i+1, bak));
        cnt.push(2*bak);
    }
    let mut offset = 0;
    for (i, &k) in cnt.iter().enumerate().rev() {
        while k <= l {
            l -= k;
            edges.push((i as usize, 19, offset));
            offset += k;
        }
    }
    assert_eq!(l, 0);
    println!("20 {}", edges.len());
    for &(a, b, w) in &edges {
        println!("{} {} {}", a+1, b+1, w);
    }
}