#include "bits/stdc++.h"
#pragma warning(disable:4996)
using namespace std;
using ld = long double;
const ld eps = 1e-9;

#include<unordered_map>



const int mod = 998244353;
struct Mod {
public:
	int num;
	Mod() : Mod(0) { ; }
	Mod(long long int n) : num((n % mod + mod) % mod) {
		static_assert(mod<INT_MAX / 2, "mod is too big, please make num 'long long int' from 'int'");
	}
	Mod(int n) : Mod(static_cast<long long int>(n)) { ; }
	operator int() { return num; }
};

Mod operator+(const Mod a, const Mod b) { return Mod((a.num + b.num) % mod); }
Mod operator+(const long long int a, const Mod b) { return Mod(a) + b; }
Mod operator+(const Mod a, const long long int  b) { return b + a; }
Mod operator++(Mod &a) { return a + Mod(1); }
Mod operator-(const Mod a, const Mod b) { return Mod((mod + a.num - b.num) % mod); }
Mod operator-(const long long int a, const Mod b) { return Mod(a) - b; }
Mod operator--(Mod &a) { return a - Mod(1); }
Mod operator*(const Mod a, const Mod b) { return Mod(((long long)a.num * b.num) % mod); }
Mod operator*(const long long int a, const Mod b) { return Mod(a)*b; }
Mod operator*(const Mod a, const long long int b) { return Mod(b)*a; }
Mod operator*(const Mod a, const int b) { return Mod(b)*a; }
Mod operator+=(Mod &a, const Mod b) { return a = a + b; }
Mod operator+=(long long int &a, const Mod b) { return a = a + b; }
Mod operator-=(Mod &a, const Mod b) { return a = a - b; }
Mod operator-=(long long int &a, const Mod b) { return a = a - b; }
Mod operator*=(Mod &a, const Mod b) { return a = a * b; }
Mod operator*=(long long int &a, const Mod b) { return a = a * b; }
Mod operator*=(Mod& a, const long long int &b) { return a = a * b; }
Mod operator^(const Mod a, const int n) {
	if (n == 0) return Mod(1);
	Mod res = (a * a) ^ (n / 2);
	if (n % 2) res = res * a;
	return res;
}
Mod mod_pow(const Mod a, const long long  int n) {
	if (n == 0) return Mod(1);
	Mod res = mod_pow((a * a), (n / 2));
	if (n % 2) res = res * a;
	return res;
}

Mod inv(const Mod a) { return a ^ (mod - 2); }
Mod operator/(const Mod a, const Mod b) {
	assert(b.num != 0);
	return a * inv(b);
}
Mod operator/(const long long int a, const Mod b) {
	return Mod(a) / b;
}
Mod operator/=(Mod &a, const Mod b) {
	return a = a / b;
}

#define MAX_MOD_N 10240

Mod fact[MAX_MOD_N], factinv[MAX_MOD_N];
void init(const int amax = MAX_MOD_N) {
	fact[0] = Mod(1); factinv[0] = 1;
	for (int i = 0; i < amax - 1; ++i) {
		fact[i + 1] = fact[i] * Mod(i + 1);
		factinv[i + 1] = factinv[i] / Mod(i + 1);
	}
}
Mod comb(const int a, const int b) {
	return fact[a] * factinv[b] * factinv[a - b];
}

vector<vector<int>>flag(1001,vector<int>(1001));

Mod solve(int rest, int now,vector<vector<Mod>>&memo,const vector<int>&nums) {
	if (!flag[rest][now]) {
		flag[rest][now]=true;
		if (now == 1) {
			return memo[rest][now] = 1;
		}
		else {

			Mod ans = 0;
			Mod mo = 1;
			for (int k = 0; k <= rest / now; ++k) {

				ans += solve(rest - k*now + nums[now - 1], now - 1, memo, nums)*mo;
				mo = mo*comb(rest - k*now, now);
				mo = mo / Mod(k + 1);
			}

			return memo[rest][now] = ans;
		}
	}
	else {
		return memo[rest][now];
	}
}
int main() {
	while (true) {

		int N; cin >> N;
		if(!N)break;
		vector<long long int>odds, as;
		for (int i = 0; i < N*(N + 1)/2; ++i) {
			long long int a; cin >> a;
			if (a % 2)odds.push_back(a);
			else as.push_back(a);
		}
		sort(odds.begin(), odds.end());
		sort(as.begin(), as.end());

		long long int ans = round(sqrt(ld(as[as.size() - 1])*as[as.size() - 2] / odds.back()) + eps);

		vector<long long int>ans2;
		for (int i = 0; i < N; ++i) {
			ans2.push_back(as[i] / ans);
		}
		cout << ans << endl;
		for (int i = 0; i < N; ++i) {
			cout << ans2[i];
			if(i==N-1)cout<<endl;
			else cout<<" ";
		}
	}
	
	return 0;

}

### Prompt

In Cpp, your task is to solve the following problem:

Problem H: Squid Multiplication

Squid Eiko loves mathematics. Especially she loves to think about integer. One day, Eiko found a math problem from a website.

"A sequence b ={ai + aj | i < j } is generated from a sequence a ={a0 , ... , an | ai is even if i is 0, otherwise ai is odd}. Given the sequence b , find the sequence a ."

This problem is easy for Eiko and she feels boring. So, she made a new problem by modifying this problem .

"A sequence b ={ai *aj | i < j } is generated from a sequence a ={ a0, ... , an | ai is even if  i  is 0, otherwise ai is odd}. Given the sequence b , find the sequence a ."

Your task is to solve the problem made by Eiko.



Input

Input consists of multiple datasets.
Each dataset is given by following formats.


n
b0 b1 ... bn*(n+1)/2-1


n is the number of odd integers in the sequence a. The range of n is 2 ≤ n ≤ 250. bi is separated by a space. Each bi is 1 ≤ bi ≤ 263-1. The end of the input consists of a single 0.

Output

For each dataset, you should output two lines. First line contains a0, an even number in the sequence a. The second line contains n odd elements separated by a space. The odd elements are sorted by increasing order. You can assume that the result is greater than or equal to 1 and less than or equal to 231-1.

Example

Input

3
6 10 14 15 21 35
2
30 42 35
0


Output

2
3 5 7
6
5 7

### Response

```cpp
#include "bits/stdc++.h"
#pragma warning(disable:4996)
using namespace std;
using ld = long double;
const ld eps = 1e-9;

#include<unordered_map>



const int mod = 998244353;
struct Mod {
public:
	int num;
	Mod() : Mod(0) { ; }
	Mod(long long int n) : num((n % mod + mod) % mod) {
		static_assert(mod<INT_MAX / 2, "mod is too big, please make num 'long long int' from 'int'");
	}
	Mod(int n) : Mod(static_cast<long long int>(n)) { ; }
	operator int() { return num; }
};

Mod operator+(const Mod a, const Mod b) { return Mod((a.num + b.num) % mod); }
Mod operator+(const long long int a, const Mod b) { return Mod(a) + b; }
Mod operator+(const Mod a, const long long int  b) { return b + a; }
Mod operator++(Mod &a) { return a + Mod(1); }
Mod operator-(const Mod a, const Mod b) { return Mod((mod + a.num - b.num) % mod); }
Mod operator-(const long long int a, const Mod b) { return Mod(a) - b; }
Mod operator--(Mod &a) { return a - Mod(1); }
Mod operator*(const Mod a, const Mod b) { return Mod(((long long)a.num * b.num) % mod); }
Mod operator*(const long long int a, const Mod b) { return Mod(a)*b; }
Mod operator*(const Mod a, const long long int b) { return Mod(b)*a; }
Mod operator*(const Mod a, const int b) { return Mod(b)*a; }
Mod operator+=(Mod &a, const Mod b) { return a = a + b; }
Mod operator+=(long long int &a, const Mod b) { return a = a + b; }
Mod operator-=(Mod &a, const Mod b) { return a = a - b; }
Mod operator-=(long long int &a, const Mod b) { return a = a - b; }
Mod operator*=(Mod &a, const Mod b) { return a = a * b; }
Mod operator*=(long long int &a, const Mod b) { return a = a * b; }
Mod operator*=(Mod& a, const long long int &b) { return a = a * b; }
Mod operator^(const Mod a, const int n) {
	if (n == 0) return Mod(1);
	Mod res = (a * a) ^ (n / 2);
	if (n % 2) res = res * a;
	return res;
}
Mod mod_pow(const Mod a, const long long  int n) {
	if (n == 0) return Mod(1);
	Mod res = mod_pow((a * a), (n / 2));
	if (n % 2) res = res * a;
	return res;
}

Mod inv(const Mod a) { return a ^ (mod - 2); }
Mod operator/(const Mod a, const Mod b) {
	assert(b.num != 0);
	return a * inv(b);
}
Mod operator/(const long long int a, const Mod b) {
	return Mod(a) / b;
}
Mod operator/=(Mod &a, const Mod b) {
	return a = a / b;
}

#define MAX_MOD_N 10240

Mod fact[MAX_MOD_N], factinv[MAX_MOD_N];
void init(const int amax = MAX_MOD_N) {
	fact[0] = Mod(1); factinv[0] = 1;
	for (int i = 0; i < amax - 1; ++i) {
		fact[i + 1] = fact[i] * Mod(i + 1);
		factinv[i + 1] = factinv[i] / Mod(i + 1);
	}
}
Mod comb(const int a, const int b) {
	return fact[a] * factinv[b] * factinv[a - b];
}

vector<vector<int>>flag(1001,vector<int>(1001));

Mod solve(int rest, int now,vector<vector<Mod>>&memo,const vector<int>&nums) {
	if (!flag[rest][now]) {
		flag[rest][now]=true;
		if (now == 1) {
			return memo[rest][now] = 1;
		}
		else {

			Mod ans = 0;
			Mod mo = 1;
			for (int k = 0; k <= rest / now; ++k) {

				ans += solve(rest - k*now + nums[now - 1], now - 1, memo, nums)*mo;
				mo = mo*comb(rest - k*now, now);
				mo = mo / Mod(k + 1);
			}

			return memo[rest][now] = ans;
		}
	}
	else {
		return memo[rest][now];
	}
}
int main() {
	while (true) {

		int N; cin >> N;
		if(!N)break;
		vector<long long int>odds, as;
		for (int i = 0; i < N*(N + 1)/2; ++i) {
			long long int a; cin >> a;
			if (a % 2)odds.push_back(a);
			else as.push_back(a);
		}
		sort(odds.begin(), odds.end());
		sort(as.begin(), as.end());

		long long int ans = round(sqrt(ld(as[as.size() - 1])*as[as.size() - 2] / odds.back()) + eps);

		vector<long long int>ans2;
		for (int i = 0; i < N; ++i) {
			ans2.push_back(as[i] / ans);
		}
		cout << ans << endl;
		for (int i = 0; i < N; ++i) {
			cout << ans2[i];
			if(i==N-1)cout<<endl;
			else cout<<" ";
		}
	}
	
	return 0;

}

```