#include <bits/stdc++.h>
#include <math.h>
			
using namespace std;

// c++ short types
#define Int long long
#define vt vector

const Int inf = 1e17+1;

const int nmax = 5000;
Int dp[nmax][nmax];
map<Int, vt<array<Int, 2>>> vals;
void precalc() {
	memset(dp, 0, sizeof(dp));
	for(int n = 0; n < nmax; ++n) {
		for(int k = 0; k <= n; ++k) {
			if(k == 0){
				dp[n][k] = 1;
			} else {
				dp[n][k] = dp[n-1][k] + dp[n-1][k-1];
			}
			dp[n][k] = min(dp[n][k], inf);
			if(dp[n][k] < inf && k != 0 && k != n) {
				vals[dp[n][k]].push_back({n, k});
			}
		}
	}
}

void solver() {
	Int m; cin >> m;
	set<array<Int, 2>> pairs;
	auto cnk = [&](Int n, Int k) -> Int {
		if(n <= k) {
			return 0;
		}
		if(n < nmax) {
			return dp[n][k];
		}
		if(k > n - k) {
			k = n-k;
		}
		__int128 fact = 1;
		for(__int128 i = 1; i <= k; ++i) {
			fact *= i;
		}
		__int128 value = 1;
		for(__int128 i = 0; i < k; ++i) {
			value *= (n-i);
			if(value / fact > inf) {
				return inf;
			}
		}
		return value / fact;
	};
	for(Int k = 1; k <= min(10ll, m); ++k) {
		Int fact = 1;
		for(int i = 1; i <= k; ++i) {
			fact *= 1;
		}
		auto f = [&](Int n) -> Int {
			if(n <= k) {
				return 0ll;
			}
			__int128 value = 1;
			for(__int128 i = 0; i < k; ++i) {
				// value * (n-i) / fact > inf
				// value / fact * (n-i) > inf
				value *= (n-i);
				if(value / fact > inf) {
					return inf;
				}
			}
			return value / fact;
		};
		Int l = 0, r = m + 1;
		assert(f(r) > m and f(l) <= m);
		while(r - l > 1) {
			Int med = (l+r)>>1;
			if(cnk(med, k) <= m) {
				l = med;
			} else {
				r = med;
			}
		}
		if(cnk(l, k) == m) {
			pairs.insert({l, k});
			pairs.insert({l, l-k});
		}
	}
	for(auto p : vals[m]) {
		pairs.insert(p);
	}
	cout << pairs.size() << "\n";
	for(auto [a, b] : pairs) {
		cout << "(" << a << "," << b << ") ";
		assert(cnk(a, b) == m);
	}
	cout << "\n";
}

int main()
{
	precalc();
	ios::sync_with_stdio(false); cin.tie(nullptr);
	int tt = 1;
	cin >> tt;
	for(int t = 0; t < tt; ++t) {
    solver();
	}
	return 0;
}