using System;
using System.Collections.Generic;

namespace A338890 {
    /// <summary>
    /// A338892		Primitive terms of A338890.
    /// </summary>
    class Program {
        /// <summary>
        /// Compute first terms of sequence A338892.
        /// </summary>
        static void Main() {
            List<long> primitive = new List<long>();
            for (long hypothenuse = 1; hypothenuse < 1000000; hypothenuse++) {
                long squareOfHypothenuse = hypothenuse * hypothenuse;
                Squares[squareOfHypothenuse] = hypothenuse;
                PythagoreanTriangles[hypothenuse] = new List<PythagoreanTriangle>();

                long squareOfLeftLeg;
                for (long leftLeg = 1; 2*(squareOfLeftLeg=leftLeg*leftLeg)<=squareOfHypothenuse; leftLeg++) {
                    long squareOfRightLeg = squareOfHypothenuse - squareOfLeftLeg;
                    long rightLeg;
                    if (Squares.TryGetValue(squareOfRightLeg, out rightLeg)) {
                        PythagoreanTriangle triangle = new PythagoreanTriangle() {
                            Hypothenuse = hypothenuse,
                            LeftLeg = leftLeg,
                            RightLeg = rightLeg,
                        };
                        PythagoreanTriangles[hypothenuse].Add(triangle);
                        PythagoreanTriangles[hypothenuse].Add(triangle.Flip);
                    }
                }

                if (IsOK(hypothenuse)) {
                    bool keep = true;
                    foreach (long p in primitive) {
                        if (hypothenuse%p==0) {
                            keep = false;
                            break;
                        }
                    }
                    if (keep) {
                        primitive.Add(hypothenuse);
                        Console.WriteLine($"{primitive.Count} {hypothenuse}");
                    }
                }
            }
        }

        /// <summary>
        /// Is hypothenuse OK?
        /// </summary>
        /// <param name="hypothenuse">hypothenuse of triangle</param>
        /// <returns>OK?</returns>
        static bool IsOK(long hypothenuse) {
            foreach (PythagoreanTriangle triangle in PythagoreanTriangles[hypothenuse]) {
                foreach (PythagoreanTriangle leftTriangle in PythagoreanTriangles[triangle.LeftLeg]) {
                    foreach (PythagoreanTriangle rightTriangle in PythagoreanTriangles[triangle.RightLeg]) {
                        if (leftTriangle.RightLeg == rightTriangle.LeftLeg) {
                            return true;
                        }
                    }
                }
            }

            return false;
        }

        /// <summary>
        /// Square table (key=n^2, value=n).
        /// </summary>
        static readonly Dictionary<long, long> Squares = new Dictionary<long, long>();

        /// <summary>
        /// List of pythagorean triangles indexed by hypothenuse.
        /// </summary>
        static readonly Dictionary<long, List<PythagoreanTriangle>> PythagoreanTriangles = new Dictionary<long, List<PythagoreanTriangle>>();
    }

    /// <summary>
    /// Pythagorean triangle (Top^2 = Left^2 + Right^2).
    /// </summary>
    public class PythagoreanTriangle {
        public long Hypothenuse { get; set; }
        public long LeftLeg { get; set; }
        public long RightLeg { get; set; }

        /// <summary>
        /// Triangle with bottom values flipped.
        /// </summary>
        public PythagoreanTriangle Flip {
            get {
                return new PythagoreanTriangle() {
                    Hypothenuse = this.Hypothenuse,
                    LeftLeg = this.RightLeg,
                    RightLeg = this.LeftLeg,
                };
            }
        }
    }
}