#include <bits/stdc++.h>

using namespace std;

constexpr int N = 100;

uint64_t splitmix(uint64_t x) {
  x += 0x9e3779b97f4a7c15;
  (x ^= x >> 30) *= 0xbf58476d1ce4e5b9;
  (x ^= x >> 27) *= 0x94d049bb133111eb;
  return x ^ x >> 31;
}

int n;
vector<int> nei[N];
int sz[N];
vector<int> cent;

void findcent(int v, int p) {
  bool cent = 1;
  sz[v] = 1;
  for (auto u: nei[v]) if (u != p) {
    findcent(u, v);
    sz[v] += sz[u];
    cent &= sz[u] * 2 <= n;
  }
  if (cent && sz[v] * 2 >= n) ::cent.push_back(v);
}

uint64_t h[N];
bool ok;

uint64_t treehash(int v, int p) {
  if (!ok) return 0;
  uint64_t x = 0;
  for (auto u: nei[v]) if (u != p) x += treehash(u, v);
  for (auto u: nei[v]) if (u != p && ok)
  for (auto w: nei[v]) if (w != p) if (w == u) break; else ok &= h[w] != h[u];
  return h[v] = splitmix(x);
}

vector<vector<int>> rooted[N];
vector<vector<int>> unrooted[N];
set<uint64_t> urs;

void build(vector<int> p, int n, int m, int i, auto f) {
  if (!n) f(p);
  if (m > n) return;
  while (++i < rooted[m].size()) {
    auto t = rooted[m][i];
    for (auto& x: t) x += p.size() + 1;
    t.insert(t.begin(), 0);
    t.insert(t.begin(), p.begin(), p.end());
    build(t, n - m, m, i, f);
  }
  build(p, n, m + 1, -1, f);
}

constexpr int W = 1e6 + 1;

int can[W], last[W];

int main() {
  cin.tie(0)->sync_with_stdio(0);
  rooted[1] = {{}};
  unrooted[1] = {{}};
  int nr = 1, nu = 1, su = 1;
  for (n = 2; nr < 1000000; nr += rooted[n].size(), nu += unrooted[n].size(), su += unrooted[n].size() * n, ++n)
  build({}, n - 1, 0, -1, [&](auto p) {
    for (int i = 0; i < n; ++i) nei[i].clear();
    for (int i = 1; i < n; ++i) nei[i].push_back(p[i - 1]), nei[p[i - 1]].push_back(i);
    rooted[n].push_back(p);
    ok = 1;
    cent.clear();
    findcent(0, 0);
    uint64_t h = treehash(cent[0], cent.back()), hh = h;
    if (ok && (cent.size() == 1 || h != (hh = treehash(cent[1], cent[0]))) && ok && urs.insert(h + hh).second) unrooted[n].push_back(p);
  });
  for (int w = 0; ++w < 22; )
  for (int i = W; i--; ) if (can[i] || !i)
  for (int c = 1, ww = i + w; ww < W && c <= unrooted[w].size() && can[ww] < can[i] + c; ++c, ww += w) can[ww] = can[i] + c, last[ww] = w;
  int n; cin >> n;
  if (n > 1 && n < 6) return cout << "NO", 0;
  cout << "YES\n";
  if (n == 6) {
    cout << "6\n1 2\n2 3\n1 3\n3 4\n2 5\n5 6\n";
    return 0;
  }
  cout << n - can[n] << '\n';
  int d = 0;
  while (n) {
    auto p = unrooted[last[n]].back(); unrooted[last[n]].pop_back();
    for (int i = 0; i < p.size(); ++i) cout << d + i + 2 << ' ' << d + p[i] + 1 << '\n';
    d += last[n];
    n -= last[n];
  }
}