#include <bits/stdc++.h>

using namespace std;

const int N = 1e6 + 5, K = 23;
const int limit[] = {1000000, 1, 0, 0, 0, 0, 0, 1, 1, 3, 6, 15, 29, 67, 139, 310, 667, 1480, 3244, 7241, 16104};

int n, m = 20;
vector<string> t1[K], t0[K];
int f[K][N], pre[K][N];
int q[N], hh, tt;
int pid;
vector<pair<int, int> > e;

inline bool CornerCases(int n)
{
    if(n == 1) return puts("YES\n0"), 1;
    if(n <= 5) return puts("NO"), 1;
    if(n == 6)
    {
        puts("YES");
        puts("6");
        puts("1 2");
        puts("1 3");
        puts("2 3");
        puts("1 4");
        puts("4 5");
        puts("2 6");
        return 1;
    }
    return 0;
}

inline void DFS(int n, string now, int siz, int lim, int pos, int ty, vector<string> &t)
{
    if((int)t.size() >= limit[ty]);
    if((int)now.size() > n * 2) return ;
    if((int)now.size() == n * 2)
    {
        t.push_back("(" + now + ")");
        return ;
    }
    if(siz > lim) return ;
    DFS(n, now, siz + 1, lim, 0, ty, t);
    for(int i = pos; i < (int)t1[siz].size(); i ++ )
        DFS(n, now + t1[siz][i], siz, lim, i + 1, ty, t);
}
inline void SearchRootedTrees(int k)
{
    t1[1].push_back("()");
    for(int i = 2; i <= k; i ++ ) DFS(i - 1, "", 1, i - 1, 0, 0, t1[i]);
}
inline void SearchUnrootedTrees(int k)
{
    t0[1].push_back("()");
    for(int i = 2; i <= k; i ++ )
    {
        DFS(i - 1, "", 1, (i - 1) / 2, 0, i, t0[i]);
        if(~i & 1)
        {
            for(int j = 0; j < (int)t1[i / 2].size(); j ++ )
            {
                for(int k = j + 1; k < (int)t1[i / 2].size(); k ++ )
                {
                    t0[i].push_back(t1[i / 2][j]);
                    t0[i].back().pop_back();
                    t0[i].back() += t1[i / 2][k] + ")";
                    if((int)t0[i].size() == limit[i]) break;
                }
                if((int)t0[i].size() == limit[i]) break;
            }
        }
    }
}

inline void DP(int n)
{
    memset(f[1], -0x3f, sizeof f[1]);
    f[1][0] = 0, f[1][1] = 1;
    for(int i = 2; i <= m; i ++ )
    {
        int c = t0[i].size();
        for(int j = 0; j < i; j ++ )
        {
            f[i][j] = f[i - 1][j], pre[i][j] = j;
            hh = tt = 0, q[0] = 0;
            for(int k = 1; k <= (n - j) / i; k ++ )
            {
                while(hh <= tt && q[hh] < k - c) hh ++ ;
                while(hh <= tt && f[i - 1][q[tt] * i + j] - q[tt] <= f[i - 1][k * i + j] - k) tt -- ;
                q[ ++ tt] = k;
                f[i][k * i + j] = f[i - 1][q[hh] * i + j] + k - q[hh];
                pre[i][k * i + j] = q[hh] * i + j;
            }
        }
    }
}

inline int GetTree(string &str, int l, int r)
{
    int u = ++ pid;
    for(int j = l + 1, k; j < r; j = k)
    {
        k = j + 1;
        int s = 1;
        while(s)
        {
            s += str[k] == '(' ? 1 : -1;
            k ++ ;
        }
        e.emplace_back(u, GetTree(str, j, k - 1));
    }
    return u;
}

int main()
{
    scanf("%d", &n);
    if(CornerCases(n)) return 0;
    SearchRootedTrees(m / 2);
    SearchUnrootedTrees(m);
    DP(n);
    for(int i = m, j = n; i >= 1; i -- )
    {
        int c = (j - pre[i][j]) / i;
        for(int k = 0; k < c; k ++ ) GetTree(t0[i][k], 0, i * 2 - 1);
        j = pre[i][j];
    }
    puts("YES");
    printf("%d\n", (int)e.size());
    for(pair<int, int> i : e) printf("%d %d\n", i.first, i.second);
    return 0;
}