# ZeroJudge - f289: 求極限
### 題目連結：https://zerojudge.tw/ShowProblem?problemid=f289
###### tags: `ZeroJudge` `數學`

#include <iostream>
#include <sstream>
using namespace std;

stringstream ss;
string respect, fuction[2];
int coefficients[2][3], fuctionAmount;

string Evaluate(int index) {
	if (respect == "-inf" || respect == "inf")
		return coefficients[index][2] || coefficients[index][1] ? respect : to_string(coefficients[index][0]);
	int sums = 0, base = 1, power = stoi(respect);
	for (int i = 0; i < 3; ++i, base *= power)
		sums += coefficients[index][i] * base;
	return to_string(sums);
}

void Analyze(int index) {
	static string term;
	static int coefficient;
	ss.clear(); ss.str(""); ss << fuction[index];
	for (int i = 0; i < 3; ++i)
		coefficients[index][i] = 0;
	while (ss >> coefficient) 
		coefficients[index][ss >> term ? (term == "x^2" ? 2 : 1) : 0] = coefficient;
}

void Differentiate(int index) {
	for (int i = 0; i < 2; ++i)
		coefficients[index][i] = coefficients[index][i + 1] * (i + 1);
	coefficients[index][2] = 0;
}

void DertemineLimit() {
	static string out1, out2;
	if (fuctionAmount == 1) {
		out1 = Evaluate(0);
		cout << (out1 == "inf" || out1 == "-inf" ? "limit doesn't exist" : out1) << '\n';
	}
	else {
		do {
			out1 = Evaluate(0); out2 = Evaluate(1);
			if (((out1 == "inf" || out1 == "-inf") && (out2 == "inf" || out2 == "-inf")) || (out1 == "0" && out2 == "0"))
				Differentiate(0), Differentiate(1);
			else if (out2 == "inf" || out2 == "-inf") {
				cout << "0\n";
				break;
			}
			else if (out2 == "0" || out1 == "inf" || out1 == "-inf") {
				cout << "limit doesn't exist\n";
				break;
			}
			else {
				cout << stoi(out1) / stoi(out2) << '\n';
				break;
			}
		} while (1);
	}
}

int main() {
	cin.sync_with_stdio(false), cin.tie(nullptr);
	while (cin >> respect >> ws) {
		getline(cin, fuction[0]); fuctionAmount = 1;
		for (int i = 0; i != fuction[0].size(); ++i)
			if (fuction[0][i] == '/') {
				fuction[1] = fuction[0].substr(i + 2);
				fuction[0] = fuction[0].substr(0, i - 1);
				++fuctionAmount;
				break;
			}
		for (int i = 0; i < fuctionAmount; ++i)
			Analyze(i);
		DertemineLimit();
	}
}