With the motto "Creating your own path," a shrine created a fortune-telling fortune with its own hands. Ask the person who draws the lottery to throw six stones first, then the line segment connecting the first and second of the thrown stones, the line segment connecting the third and fourth, the fifth and six The fortune is determined from the area of ​​the triangle whose apex is the intersection of the three line segments connecting the second line segment. The relationship between each fortune and the area of ​​the triangle is as follows.

Area of ​​a triangle whose apex is the intersection of line segments | Fortune
--- | ---
Over 1,900,000 | Daikichi
1,000,000 or more and less than 1,900,000 | Nakayoshi (chu-kichi)
100,000 or more and less than 1,000,000 | Kichi
Greater than 0 and less than 100,000 | Kokichi (syo-kichi)
No triangle | Kyo



However, the size of the area of ​​the triangle is determined by the priest by hand, so it cannot be said to be accurate and it takes time. So, as an excellent programmer living in the neighborhood, you decided to write a program as soon as possible to help the priest.

Create a program that takes the information of three line segments as input and outputs the fortune from the area of ​​the triangle whose vertices are the intersections of the line segments. The line segment information is given the coordinates of the start point (x1, y1) and the coordinates of the end point (x2, y2), and the coordinates of the start point and the end point must be different. Also, if two or more line segments are on the same straight line, if there are two line segments that do not have intersections, or if three line segments intersect at one point, it is "no triangle".

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Input

A sequence of multiple datasets is given as input. The end of the input is indicated by four zero lines. Each dataset is given in the following format:


line1
line2
line3


The i-th line is given the information of the i-th line segment. Information for each line is given in the following format.


x1 y1 x2 y2


Integers (x1, y1), (x2, y2) (-1000 ≤ x1, y1, x2, y2 ≤ 1000) representing the coordinates of the endpoints of the line segment are given, separated by blanks.

Output

The result of the fortune telling is output to one line for each data set.

Example

Input

-3 -2 9 6
3 -2 7 6
-1 0 5 0
2 2 -1 -1
0 1 2 1
-3 -1 3 1
0 0 0 0


Output

syo-kichi
kyo
import java.util.Scanner;


public class Main {

	
	public static void main(String args[]){
		Scanner sc = new Scanner(System.in);
		
		while(true){
			final int x1 = sc.nextInt();
			final int y1 = sc.nextInt();
			final int x2 = sc.nextInt();
			final int y2 = sc.nextInt();
			
			if(x1 == 0 && y1 == 0 && x2 == 0 && y2 == 0){
				break;
			}
			
			Point2D[][] lines = new Point2D[3][2];
			
			lines[0][0] = new Point2D(x1, y1);
			lines[0][1] = new Point2D(x2, y2);
			lines[1][0] = new Point2D(sc.nextInt(), sc.nextInt());
			lines[1][1] = new Point2D(sc.nextInt(), sc.nextInt());
			lines[2][0] = new Point2D(sc.nextInt(), sc.nextInt());
			lines[2][1] = new Point2D(sc.nextInt(), sc.nextInt());
			
			Point2D[] crosses = new Point2D[3];
			boolean not_found = false;
			for(int i = 0; i < 3; i++){
				if(Point2D.intersect_s(lines[i][0], lines[i][1], lines[i + 1 >= 3 ? 0 : (i + 1)][0], lines[i + 1 >= 3 ? 0 : (i + 1)][1])){
					crosses[i] = Point2D.interpoint_s(lines[i][0], lines[i][1], lines[i + 1 >= 3 ? 0 : (i + 1)][0], lines[i + 1 >= 3 ? 0 : (i + 1)][1]);
				}else{
					crosses[i] = null;
					not_found = true;
				}
				//System.out.println(crosses[i]);
			}
			
			if(not_found){
				System.out.println("kyo");
				continue;
			}
			
			boolean same = false;
			for(int i = 0; i < 3; i++){
				if(crosses[i].equals(crosses[i + 1 >= 3 ? 0 : (i + 1)])){
					same = true;
					break;
				}
			}
			
			if(same){
				System.out.println("kyo");
				continue;
			}
			
			double S = Point2D.area(crosses[0], crosses[1], crosses[2]);
			//System.out.println(S);
			if(S >= 1900000){
				System.out.println("dai-kichi");
			}else if(S >= 1000000){
				System.out.println("chu-kichi");
			}else if(S >= 100000){
				System.out.println("kichi");
			}else if(Double.isNaN(S)){
				System.out.println("kyo");
			}else{
				System.out.println("syo-kichi");
			}
			
			//なぜかテストケース通らない
		}
		
	}
}

class Point2D {
	public double x;
	public double y;

	public static final double EPS = 1e-9;

	public Point2D(double x, double y) {
		this.x = x;
		this.y = y;
	}

	public Point2D(Point2D point) {
		this.x = point.x;
		this.y = point.y;
	}

	public String toString() {
		return x + "," + y;
	}

	@Override
	public boolean equals(Object o) {
		if (o instanceof Point2D) {
			Point2D another = (Point2D) o;
			if (this.x - EPS < another.x && this.x + EPS > another.x
					&& this.y - EPS < another.y && this.y + EPS > another.y) {
				return true;
			}
			
			return false;

			// return this.x == another.x && this.y == another.y;
		}
		return false;
	}

	public Point2D add(double x, double y) {
		return new Point2D(this.x + x, this.y + y);
	}

	public Point2D sub(double x, double y) {
		return add(-x, -y);
	}

	public Point2D add(Point2D another) {
		return add(another.x, another.y);
	}

	public Point2D sub(Point2D another) {
		return sub(another.x, another.y);
	}

	public Point2D mul(double d) {
		return new Point2D(this.x * d, this.y * d);
	}

	public Point2D div(double d) {
		return new Point2D(this.x / d, this.y / d);
	}

	public double dot(double x, double y) {
		return this.x * x + this.y * y;
	}

	public double dot(Point2D another) {
		return dot(another.x, another.y);
	}

	public double cross(double x, double y) {
		return this.x * y - this.y * x;
	}

	public double cross(Point2D another) {
		return cross(another.x, another.y);
	}

	public double dist(double x, double y) {
		return Math.sqrt((this.x - x) * (this.x - x) + (this.y - y)
				* (this.y - y));
	}

	public double dist(Point2D another) {
		return dist(another.x, another.y);
	}

	public double dist_o() {
		return dist(0, 0);
	}

	public Point2D unit() {
		return div(dist_o());
	}

	public boolean pol(Point2D start, Point2D end) {
		return end.sub(start).cross(this.sub(start)) < EPS;
	}

	public boolean pos(Point2D start, Point2D end) {
		return (start.dist(this) + this.dist(end) < start.dist(end) + EPS);
	}

	public double pld(Point2D start, Point2D end) {
		return Math.abs((end.sub(start).cross(this.sub(start)))
				/ end.sub(start).dist_o());
	}

	public double psd(Point2D start, Point2D end) {
		if (end.sub(start).dot(this.sub(start)) < EPS) {
			return this.dist(start);
		} else if (start.sub(end).dot(this.sub(end)) < EPS) {
			return this.dist(end);
		} else {
			return end.sub(start).cross(this.sub(start)) / end.dist(start);
		}
	}

	public static boolean intersect_s(Point2D a1, Point2D a2, Point2D b1,
			Point2D b2) {
		return (a2.sub(a1).cross(b1.sub(a1)) * a2.sub(a1).cross(b2.sub(a1)) < EPS)
				&& (b2.sub(b1).cross(a1.sub(b1)) * b2.sub(b1).cross(a2.sub(b1)) < EPS);
	}

	public static boolean insersect_l(Point2D a1, Point2D a2, Point2D b1,
			Point2D b2) {
		return a1.sub(a2).cross(b1.sub(b2)) < EPS;
	}

	public static Point2D interpoint_s(Point2D a1, Point2D a2, Point2D b1,
			Point2D b2) {
		Point2D b = b2.sub(b1);
		double d1 = Math.abs(b.cross(a1.sub(b1)));
		double d2 = Math.abs(b.cross(a2.sub(b1)));
		double t = d1 / (d1 + d2);
		Point2D a = a2.sub(a1), v = a.mul(t);
		return a1.add(v);
	}

	public static Point2D interpoint_l(Point2D a1, Point2D a2, Point2D b1,
			Point2D b2) {
		Point2D a = a2.sub(a1);
		Point2D b = b2.sub(b1);
		double t = b.cross(b1.sub(a1)) / b.cross(a);
		Point2D v = a.mul(t);
		return a1.add(v);
	}

	public static Point2D[] cross_ss(Point2D p1, double r1, Point2D p2,
			double r2) {
		double dis = p1.dist(p2);

		if (r1 + EPS > r2 && r1 - EPS < r2 && dis < EPS) {
			return new Point2D[0]; // same
		}

		if (dis - EPS < r1 + r2 && dis + EPS > r1 + r2) {
			Point2D tmp = p2.sub(p1);
			tmp = tmp.mul(r1 / tmp.dist_o());
			Point2D ret[] = new Point2D[1];
			ret[0] = p1.add(tmp);
			return ret;
		} else if (dis + EPS > r1 + r2) {
			return new Point2D[0]; // out
		}

		double dis_m = Math.abs(r1 - r2);

		if (dis_m + EPS > dis && dis_m - EPS < dis) {
			Point2D tmp = null;
			if (r1 > r2) {
				tmp = p2.sub(p1);
			} else {
				tmp = p1.sub(p2);
			}

			double min = Math.min(r1, r2);

			tmp = tmp.mul((min + tmp.dist_o()) / tmp.dist_o());

			Point2D ret[] = new Point2D[1];
			ret[0] = p1.add(tmp);
			return ret;
		} else if (dis_m + EPS > dis) {
			return new Point2D[0]; // inner
		} else {
			Point2D ret[] = new Point2D[2];

			double theta = Math.acos((dis * dis + r1 * r1 - r2 * r2)
					/ (2 * dis * r1));
			double a = Math.atan2(p2.y - p1.y, p2.x - p1.x);

			ret[0] = new Point2D(r1 * Math.cos(a + theta) + p1.x, r1
					* Math.sin(a + theta) + p1.y);
			ret[1] = new Point2D(r1 * Math.cos(a - theta) + p1.x, r1
					* Math.sin(a - theta) + p1.y);
			return ret;
		}
	}

	public void interpoint_lc(Point2D start, Point2D end, Point2D c, double r,
			Point2D ans[]) {
		if (c.pld(start, end) > r + EPS)
			return;
		Point2D v = end.sub(start).unit();
		double delta = v.dot(start.sub(c)) * v.dot(start.sub(c))
				- start.dist(c) * start.dist(c) + r * r;
		double t = -v.dot(start.sub(c));
		double s = Math.sqrt(delta);
		ans[0] = start.add(v.mul(t + s));
		ans[1] = start.add(v.mul(t + s));
	}

	public Point2D normal_vector(Point2D p, Point2D a, Point2D b) {
		Point2D v = b.sub(a).unit();
		v = v.cross(p.sub(a)) > 0 ? new Point2D(v.y, (-1) * v.x) : new Point2D(
				(-1) * v.y, v.x);
		return v.mul(p.pld(a, b));
	}

	public static double area(Point2D a, Point2D b, Point2D c) {
		return Math.abs((c.sub(a).cross(b.sub(a))) * 0.5);
	}

}