#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

inline ll rd() {
    ll x = 0;
    bool f = 0;
    char c = getchar();
    for (; !isdigit(c); c = getchar()) f |= (c == '-');
    for (; isdigit(c); c = getchar()) x = x * 10 + (c ^ 48);
    return f ? -x : x;
}

#define eb emplace_back
#define all(s) (s).begin(), (s).end()
#define rep(i, a, b) for (int i = (a); i <= (b); ++i)
#define per(i, a, b) for (int i = (a); i >= (b); --i)

double fac[31];

ll gcd(ll a, ll b) {return b ? gcd(b, a % b) : a;}

inline void work() {
    ll w = rd();
    vector<pll> ans;
    auto check = [&](ll n, ll m) {
        vector<ll> tmp, tmp2;
        tmp.eb(w);
        rep(i, 1, m) tmp.eb(i);
        rep(i, 1, m) {
            tmp2.clear();
            ll cur = n - i + 1;
            for (auto x : tmp) {
                ll g = gcd(x, cur);
                cur /= g; x /= g;
                if (x) tmp2.eb(x);
            }
            if (cur != 1) return;
            swap(tmp, tmp2);
        }
        for (auto x : tmp) if (x != 1) return;
        ans.eb(n, m); ans.eb(n, n - m);
    };
    rep(i, 1, 30) {
        double bound = pow(w * fac[i], 1.0 / i);
        ll L = max(i * 2ll, (ll)bound - 20);
        ll R = bound + 20;
        // cout << i << " : " << L << " " << R << endl;
        for (ll j = L; j <= R; ++j) check(j, i);
    }
    sort(all(ans));
    ans.erase(unique(all(ans)), ans.end());
    printf("%d\n", (int)ans.size());
    bool first = true;
    for (auto [x, y] : ans) {
        if (!first) putchar(' ');
        first = false;
        printf("(%lld,%lld)", x, y);
    }
    puts("");
}

int main() {
    fac[0] = 1;
    rep(i, 1, 30) fac[i] = fac[i - 1] * i;
    per(t, rd(), 1) work();
    return 0;
}