#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>

using namespace std;

int X1[3];
int X2[3];
int Y1[3];
int Y2[3];

int X3[3];
int Y3[3];

void rot(int x, double ang) {
	X3[x] = (int)round(X1[x] * cos(ang) - Y1[x] * sin(ang));
	Y3[x] = (int)round(X1[x] * sin(ang) + Y1[x] * cos(ang));
}

int trr(vector<int> pi, int dx, int dy) {
	double ang = -atan2(dy, dx);
	rot(0, ang);
	rot(1, ang);
	rot(2, ang);

	int xs = 0;
	int ys = 0;
	for(int i = 0; i < 3; i++) {
		for(int j = i + 1; j < 3; j++) {
			int dx2 = X2[pi[j]] - X2[pi[i]];
			int dx3 = X3[j] - X3[i];
			int dy2 = Y2[pi[j]] - Y2[pi[i]];
			int dy3 = Y3[j] - Y3[i];

			if(dx3 != 0) {
				if(dx2 == 0 || dx2 % dx3 != 0) return 0;
				int nxs = dx2 / dx3;
				if(xs && nxs != xs) return 0;
				xs = nxs;
			} else if(dx2) {
				return 0;
			}
			if(dy3 != 0) {
				if(dy2 == 0 || dy2 % dy3 != 0) return 0;
				int nys = dy2 / dy3;
				if(ys && nys != ys) return 0;
				ys = nys;
			} else if(dy2) {
				return 0;
			}
		}
	}
	if(!xs || !ys) return 4;
	return 1;
}

int main() {
	cin >> X1[0] >> Y1[0] >> X1[1] >> Y1[1] >> X1[2] >> Y1[2];
	for(int t = 1; X1[0] || Y1[0] || X1[1] || Y1[1] || X1[2] || Y1[2]; t++) {
		cin >> X2[0] >> Y2[0] >> X2[1] >> Y2[1] >> X2[2] >> Y2[2];

		int res = 0;
		vector<int> pi;
		for(int i = 0; i < 3; i++) pi.push_back(i);
		do {
			for(int dx = -10; dx <= 10; dx++) {
				res += trr(pi, dx, 10);
				res += trr(pi, dx, -10);
			}
			for(int dy = -9; dy <= 9; dy++) {
				res += trr(pi, 10, dy);
				res += trr(pi, -10, dy);
			}
		} while(next_permutation(pi.begin(), pi.end()));

		res /= 2;
		cout << "Case " << t << ": ";
		if(res == 0) {
			cout << "no solution" << endl;
		} else if(res == 1) {
			cout << "equivalent solutions" << endl;
		} else {
			cout << "inconsistent solutions" << endl;
		}

		cin >> X1[0] >> Y1[0] >> X1[1] >> Y1[1] >> X1[2] >> Y1[2];
	}


}