#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef __int128 lll;
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)

lll fac[21];

inline void work() {
    lll w = rd();
    vector<pll> ans;
    auto toolarge = [&](lll prod, lll up, lll k) {
        lll cur = 1;
        rep(i, 1, k) {
            cur = cur * up;
            if (prod < cur) return true;
            --up;
        }
        return false;
    };
    auto check = [&](ll k) {
        ll L = k, R = 1e15;
        lll prod = w * fac[k];
        if (toolarge(prod, k, k)) return;
        while (L < R) {
            ll mid = (L + R + 1) / 2;
            toolarge(prod, mid, k) ? R = mid - 1 : L = mid;
        }
        rep(i, 1, k) {
            if (prod % (L - i + 1)) return;
            prod /= L - i + 1;
        }
        if (prod == 1) {
            ans.eb(L, k);
            if (L - k != k) ans.eb(L, L - k);
        }
    };
    rep(i, 1, 20) check(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, 20) fac[i] = fac[i - 1] * i;
    per(t, rd(), 1) work();
    return 0;
}