package contest180518; import java.io.ByteArrayInputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.Arrays; import java.util.InputMismatchException; public class E5 { InputStream is; PrintWriter out; String INPUT = ""; void solve() { outer: for(int Q = ni();Q > 0;Q--){ double P = nd(); int B = (int)((P/2)*(P/2)); while(Math.sqrt(B)*2 < P)B++; int C = (int)((P-Math.sqrt(B))*(P-Math.sqrt(B))); for(int q = B+C;;q++){ // √B+√(q-B) < P // q+2√B(q-B) < P^2 // B(q-B) < ((P^2-q)/2)^2 // B^2-qB+((P^2-q)/2)^2 > 0 // q^2-(P^2-q)^2 // B = (int)((q+Math.sqrt((double)q*q-(P*P-q)*(P*P-q)))/2+1); B = (int)((q+Math.sqrt(-P*P*P*P+2*P*P*q))/2+1); C = q - B; int U = B, V = C; // √(B+h)+√(C-h) = P // B+C + 2√(B+h)(C-h) = P^2 // (B+h)(C-h) = ((P^2-B-C)/2)^2 = X // -h^2+(-B+C)h+BC = X // h^2+(B-C)h+X-BC = 0 // double X = (P*P-q); // X *= X; // // q^2-(P^2-q)^2 // // -P^4+2P^2q double Y = (-(B-C)+Math.sqrt(-P*P*P*P+2*P*P*q))/2; int low = (int)Y; U += low; V -= low; { double A = Math.sqrt(U) + Math.sqrt(V); if(Math.abs(A-P) < 0.9e-10){ out.println(2 + " " + U + " " + V); continue outer; } } U--; V++; { double A = Math.sqrt(U) + Math.sqrt(V); if(Math.abs(A-P) < 0.9e-10){ out.println(2 + " " + U + " " + V); continue outer; } } } } } void run() throws Exception { // int n = 1000, m = 99999; // Random gen = new Random(1); // StringBuilder sb = new StringBuilder(); // sb.append(n + " "); // for (int i = 0; i < n; i++) { // sb.append(gen.nextDouble() * 4000 + 8000 + " "); // } // INPUT = sb.toString(); is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new PrintWriter(System.out); long s = System.currentTimeMillis(); solve(); out.flush(); if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){ // @Override // public void run() { // long s = System.currentTimeMillis(); // solve(); // out.flush(); // if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // } // }; // t.start(); // t.join(); } public static void main(String[] args) throws Exception { new E5().run(); } private byte[] inbuf = new byte[1024]; public int lenbuf = 0, ptrbuf = 0; private int readByte() { if(lenbuf == -1)throw new InputMismatchException(); if(ptrbuf >= lenbuf){ ptrbuf = 0; try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); } if(lenbuf <= 0)return -1; } return inbuf[ptrbuf++]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; } private double nd() { return Double.parseDouble(ns()); } private char nc() { return (char)skip(); } private String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ') sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private char[] ns(int n) { char[] buf = new char[n]; int b = skip(), p = 0; while(p < n && !(isSpaceChar(b))){ buf[p++] = (char)b; b = readByte(); } return n == p ? buf : Arrays.copyOf(buf, p); } private int[] na(int n) { int[] a = new int[n]; for(int i = 0;i < n;i++)a[i] = ni(); return a; } private long[] nal(int n) { long[] a = new long[n]; for(int i = 0;i < n;i++)a[i] = nl(); return a; } private char[][] nm(int n, int m) { char[][] map = new char[n][]; for(int i = 0;i < n;i++)map[i] = ns(m); return map; } private int[][] nmi(int n, int m) { int[][] map = new int[n][]; for(int i = 0;i < n;i++)map[i] = na(m); return map; } private int ni() { return (int)nl(); } private long nl() { long num = 0; int b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); } }