#include <array>
#include <algorithm>
#include <cstdint>
#include <iostream>
#include <numeric>
#include <vector>

using namespace std;

constexpr int mod = 1e9 + 7;

auto& mul(auto&& a, auto b) { return a = a * (uint64_t) b % mod; }
int inv(int a) { for (int r = 1, b = mod - 2; ; b /= 2, mul(a, a)) if (!b) return r; else if (b % 2) mul(r, a); }

using namespace std;

struct HS {
  static constexpr int mlf = 8;
  int cap;
  vector<array<int, 2>> knx;
  vector<int> head;

  HS(): cap{4 * mlf - 1}, head(cap + 1, -1) {
  }

  void emplace(int k) {
    knx.push_back({k, head[k & cap]});
    head[k & cap] = knx.size() - 1;
    maybe_rehash();
  }

  int find(int k) {
    for (int i = head[k & cap]; ~i; i = knx[i][1]) if (knx[i][0] == k) return i;
    return -1;
  }

  void clear() {
    knx.clear();
    head.assign(cap + 1, -1);
  }

  void maybe_rehash() {
    if (knx.size() * mlf <= cap) return;
    head.assign((cap += cap + 1) + 1, -1);
    for (int i = 0; i < knx.size(); ++i) {
      knx[i][1] = head[knx[i][0] & cap];
      head[knx[i][0] & cap] = i;
    }
  }
};

vector<HS> high(1);
vector<int> inv_(1);

vector<char> done;
vector<array<int, 2>> cur;
vector<int> qs;
vector<vector<int>> ans;

void gen_high(const vector<int>& prof, int n0, int n, int c, int p) {
  high[n0 - n].emplace(p);
  int i = 0;
  for (int cc = prof[n]; ++cc <= min(n, c); ) {
    for (; i < cc; ++i) mul(p, inv_[n0 - i]);
    gen_high(prof, n0, n - cc, cc, p);
  }
}

void restore_high(const vector<int>& prof, int n0, int n, int c, auto&& cur, auto&& idx, auto&& cidx) {
  ++idx;
  while (cidx < cur.size() && ::cur[cidx][0] == idx) {
    auto [x, i] = ::cur[cidx++];
    ans[i].insert(ans[i].end(), cur.begin(), cur.end());
  }
  if (cidx == cur.size()) return;
  for (int cc = prof[n]; ++cc <= min(n, c); ) {
    cur.push_back(cc);
    restore_high(prof, n0, n - cc, cc, cur, idx, cidx);
    cur.pop_back();
  }
}

void solve(const vector<int>& prof, int n0, int n, int c, int p, auto&& cur) {
  for (int i = 0; i < qs.size(); ++i) if (!done[i] && ~high[n0 - n].find(mul(+p, qs[i]))) {
    done[i] = 1;
    ans[i] = cur;
    ::cur.push_back({high[n0 - n].find(mul(+p, qs[i])), i});
  }
  int i = 0;
  for (; n + c <= n0 && c <= prof[n + c]; ++c) {
    for (; i < c; ++i) mul(p, n0 - i);
    cur.push_back(c);
    solve(prof, n0, n + c, c, p, cur);
    cur.pop_back();
  }
}

uint64_t eval_high(vector<int> profile) {
  int N = profile.size();
  vector<uint64_t> cnt(N * N);
  cnt[N * N - 1] = 1;
  uint64_t ans = 0;
  for (int n = N; --n; )
  for (int c = N; --c; ) if (cnt[n * N + c]) {
    for (int cc = min(n, c); cc > profile[n]; cc--) {
      cnt[(n - cc) * N + cc] += cnt[n * N + c];
    }
    ans += cnt[n * N + c];
  }
  return ans;
}

uint64_t eval_low(vector<int> profile) {
  int N = profile.size();
  vector<uint64_t> cnt(N * N);
  cnt[0] = 1;
  uint64_t ans = 0;
  for (int n = 0; n < N; ++n)
  for (int c = 0; c <= n; ++c) if (cnt[n * N + c]) {
    for (int cc = max(c, 1); n + cc < N && cc <= profile[n + cc]; ++cc) {
      cnt[(n + cc) * N + cc] += cnt[n * N + c];
    }
    ans += cnt[n * N + c];
  }
  return ans;
}

uint64_t eval(vector<int> profile) {
  return eval_high(profile) + eval_low(profile);
}

vector<int> makeprof(int n, vector<int> from) {
  vector<int> prof(n + 1, 0);
  int j = n;
  for (int i = 0; i < from.size() - 1; ++i) {
    while (j >= from[i]) prof[j--] = i;
  }
  while (j >= 0) prof[j--] = n;
  return prof;
}

vector<int> getopt(int n) {
  static vector<vector<int>> precalc = [] {
    int n = 124;
    vector<vector<int>> res(n);
    vector<int> tmpl(10, n);
    while (n-- > 1) {
      int64_t bst = eval(makeprof(n, tmpl));
      for (int ch = 1; ch--; ) {
        for (int i = 1; i < tmpl.size() - 1; ++i)
        for (auto d: {-1, 1}) if (tmpl[i] + d >= 0 && tmpl[i] + d <= n + 1) {
          tmpl[i] += d;
          int64_t cur = eval(makeprof(n, tmpl));
          if (cur > bst) tmpl[i] -= d;
          else if (cur < bst) ch = 1, bst = cur;
          sort(tmpl.rbegin() + 1, tmpl.rend());
        }
      }
      res[n] = tmpl;
    }
    return res;
  }();
  return makeprof(n, precalc[n]);
}

int main() {
  int tc; cin >> tc;
  qs.resize(tc);
  ans.resize(tc);
  for (int i = 0; i < tc; ++i) {
    cin >> qs[i];
    done.push_back(qs[i] <= 2);
    qs[i] = inv(qs[i]);
  }
  for (int n = 1; !all_of(done.begin(), done.end(), identity{}); ++n) {
    inv_.push_back(inv(n));
    high.push_back({});
    for (auto& x: high) x.clear();
    cur.clear();
    gen_high(getopt(n), n, n, n, 1);
    solve(getopt(n), n, 0, 1, mul(n + 1, n + 2), vector<int>{});
    sort(cur.begin(), cur.end());
    restore_high(getopt(n), n, n, n, vector<int>{}, 0, 0);
    // cout << n << '\n';
  }
  for (int i = 0; i < tc; ++i) {
    if (qs[i] == 1) cout << "1\n";
    else {
      cout << accumulate(ans[i].begin(), ans[i].end(), 0) + 2 << "\n1 2\n";
      for (int j = 0, k = 2; j < ans[i].size(); ++j)
      while (ans[i][j]--) cout << j + 1 << ' ' << ++k << '\n';
    }
  }
}