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D.cpp
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//#pragma GCC optimize "trapv"
#pragma GCC optimize("Ofast")
#pragma GCC optimize("O3", "unroll-loops")
#pragma GCC target("avx,avx2,fma")
#include<bits/stdc++.h>
#define ll long long int
#define fab(a,b,i) for(int i=a;i<b;i++)
#define pb push_back
#define db double
#define mp make_pair
#define endl "\n"
#define f first
#define se second
#define all(x) x.begin(),x.end()
#define MOD 1000000007
#define vll vector<ll>
#define vi vector<int>
#define pii pair<int,int>
#define pll pair<ll,ll>
#define quick ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL)
ll add(ll x, ll y) {ll res = x + y; return (res >= MOD ? res - MOD : res);}
ll mul(ll x, ll y) {ll res = x * y; return (res >= MOD ? res % MOD : res);}
ll sub(ll x, ll y) {ll res = x - y; return (res < 0 ? res + MOD : res);}
ll power(ll x, ll y) {ll res = 1; x %= MOD; while (y) {if (y & 1)res = mul(res, x); y >>= 1; x = mul(x, x);} return res;}
ll mod_inv(ll x) {return power(x, MOD - 2);}
using namespace std;
int main()
{ quick;
#ifndef ONLINE_JUDGE
freopen("D:/sublime/input.txt", "r", stdin);
freopen("D:/sublime/output.txt", "w", stdout);
#endif
int t;
cin >> t;
while (t--)
{
int n;
cin >> n;
int a[n + 1];
fab(1, n + 1, i)
a[i] = i;
//cout << n + 1 << endl;
if (n <= 50)
{ vector<pii> v;
fab(1, n, i)
{
if (i == (n + 1) / 2)
continue;
v.pb({i, n});
a[i] = (a[i] + n - 1) / n;
//cout << i << " " << n << endl;
}
v.pb({n, (n + 1) / 2});
int x = (n + 1) / 2;
int y = x;
a[n] = (a[n] + x - 1) / x;
while (x > 1)
{
v.pb({(n + 1) / 2, n});
a[y] = (a[y] + a[n] - 1) / a[n];
//cout << "x:" << x << endl;
x = (x + 1) / 2;
}
int cnt1 = 0, cnt2 = 0;
fab(1, n + 1, i)
{
cnt1 += (a[i] == 1);
cnt2 += (a[i] == 2);
}
//cout << "cnt:" << cnt1 << " " << cnt2 << endl;
//assert(cnt1 == n - 1 and cnt2 == 1);
//cout << "n:" << n << endl;
cout << v.size() << endl;
for (auto i : v)
cout << i.f << " " << i.se << endl;
}
else
{
vector<pii> v;
fab(1, n, i)
{
if (i == 8 or i == 2 or i == 1)
continue;
v.pb({i, n});
a[i] = (a[i] + n - 1) / n;
}
int x = n;
while (x > 1)
{
v.pb({n, 8});
a[8] = (a[8] + a[n] - 1) / a[n];
//cout << "x:" << x << endl;
x = (x + 7) / 8;
}
x = 8;
while (x > 1)
{
v.pb({8, 2});
//cout << "x:" << x << endl;
x = (x + 1) / 2;
}
assert(v.size() <= n + 5);
cout << v.size() << endl;
for (auto i : v)
cout << i.f << " " << i.se << endl;
}
}
cerr << "time taken : " << (float)clock() / CLOCKS_PER_SEC << " secs" << endl;
return 0;
}