Problem:
Score : 700 points

Problem Statement

You are given an integer N. Determine if there exists a tree with 2N vertices numbered 1 to 2N satisfying the following condition, and show one such tree if the answer is yes.

Assume that, for each integer i between 1 and N (inclusive), Vertex i and N+i have the weight i. Then, for each integer i between 1 and N, the bitwise XOR of the weights of the vertices on the path between Vertex i and N+i (including themselves) is i.

Constraints

N is an integer.

1 \leq N \leq 10^{5}

Input

Input is given from Standard Input in the following format:

N

Output

If there exists a tree satisfying the condition in the statement, print Yes; otherwise, print No.
Then, if such a tree exists, print the 2N-1 edges of such a tree in the subsequent 2N-1 lines, in the following format:

a_{1} b_{1}
\vdots
a_{2N-1} b_{2N-1}

Here each pair (a_i, b_i) means that there is an edge connecting Vertex a_i and b_i. The edges may be printed in any order.

Sample Input 1

3

Sample Output 1

Yes
1 2
2 3
3 4
4 5
5 6

The sample output represents the following graph:

Sample Input 2

1

Sample Output 2

No

There is no tree satisfying the condition.

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

// OURL: https://atcoder.jp/contests/agc035/tasks/agc035_c
#include<bits/stdc++.h>
using namespace std;
using ll = long long;
#define REP(i,n) for(int i=0,i##_len=(n);i<i##_len;++i)
#define RREP(i,a,n) for(int i=(a),i##_len=(n);i<i##_len;++i)
#define MAT1D(V,T,a) vector<T> V (a)
#define MAT2D(V,T,a,b) vector<vector<T>> V (a, vector<T>(b))
#define MAT3D(V,T,a,b,c) vector<vector<vector<T>>> V (a, vector<vector<T>>(b, vector<T>(c)))

// http://beet-aizu.hatenablog.com/entry/2018/04/08/145516
template<typename T>
vector<T> make_v(size_t a){return vector<T>(a);}
template<typename T,typename... Ts>
auto make_v(size_t a,Ts... ts){ return vector<decltype(make_v<T>(ts...))>(a,make_v<T>(ts...)); }

template<typename T,typename V>
typename enable_if<is_class<T>::value==0>::type
fill_v(T &t,const V &v){t=v;}
template<typename T,typename V>
typename enable_if<is_class<T>::value!=0>::type
fill_v(T &t,const V &v){ for(auto &e:t) fill_v(e,v); }

template <typename A>
string to_string(A v) { bool first = true; string res = "{"; for (const auto &x : v) { if (!first) { res += ", "; } first = false; res += to_string(x); } res += "}"; return res; }

string to_string(string s) { return '"' + s + '"'; }
string to_string(const char* s) { return to_string((string) s); }
string to_string(bool b) { return (b ? "true" : "false"); }
string to_string(vector<bool>::reference b) { return to_string(bool(b)); }
template <typename A, typename B>
string to_string(pair<A, B> p) { return "(" + to_string(p.first) + ", " + to_string(p.second) + ")"; }
template <typename A>
string to_string(vector<vector<A>> v) { string res; for(const auto &x : v) {res+="\n ";res += to_string(x);} return res;}

void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) { cerr << " " << to_string(H); debug_out(T...); }

#ifdef LOCAL
#define debug(...) cerr << "[L" << to_string(__LINE__) << ":" <<#__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

void set_edge(stringstream &ss, int i, int j) {
  ss << i << " " << j << endl;
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int N;
  cin >> N;
  if (!(N & N-1)) { // N=2^n
    cout << "No" << endl;
    return 0;
  }
  stringstream ss;
  set_edge(ss, 1,2);
  set_edge(ss, 2,3);
  set_edge(ss, 3,1+N);
  set_edge(ss, 1+N,2+N);
  set_edge(ss, 2+N,3+N);
  int c = (N-3);
  if (N % 2 == 0) {
    c--;
  }
  REP(i, c / 2) {
    set_edge(ss, i+4, 1+N);
    set_edge(ss, i+5, i+4);
    set_edge(ss, i+5+N, 1+N);
    set_edge(ss, i+4+N, i+5+N);
  }
  if (N%2==0) {
    // N, 2Nを入れる必要がある.
    int p = N ^ N-1 ^ 1; // p1 < N-1
    set_edge(ss, N, N-1+N);
    if (p ^ 1) {
      set_edge(ss, N*2, p+N);
    } else {
      set_edge(ss, N*2, p);
    }
  }
  cout << "Yes" << endl;
  cout << ss.str() << endl;
  return 0;
}