using System.Diagnostics; using System; using System.Linq; using System.Numerics; using System.Collections; using System.Collections.Generic; using System.IO; using System.Text; using static Functions; using N = System.Int64; static class Program { static public void Main(string[] args) { Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }); var solver = new Solver(); solver.Solve(); Console.Out.Flush(); } } public class Solver { public void Solve() { int t = ri; var ans = new string[t]; for (int q = 0; q < t; q++) { int n = ri; var d = new Dictionary(); for (int i = 0; i < n; i++) { var f = PrimeFactoring(rl); foreach (var k in f.Keys) { if (d.ContainsKey(k)) d[k] ^= (int)(f[k] & 1); else d.Add(k, (int)(f[k] & 1)); } } bool ok = true; foreach (var p in d.Keys) ok &= d[p] == 0; ans[q] = ok ? "Yes" : "No"; } WriteJoin("\n", ans); } bool IsPrimeMR(long n) { if ((n & 1) == 0) return n == 2; long s = 0, d = n - 1; while ((d & 1) == 0) { s++; d >>= 1; } var aarr = new long[] { 2, 325, 9375, 28178, 450775, 9780504, 1795265022 }; foreach (var a in aarr) { long p = 1; long x = a; var c = d; while (c > 0) { if ((c & 1) == 1) p *= x; x = x * x % n; c >>= 1; } if (p == 1) continue; bool no = true; for (int i = 0; i < s; i++) { p = p * p % n; if (p == n - 1) { no = false; break; } } if (no) return false; } return true; } long FindFactorRho(long n) { long m = 1; while (m * m * m * m * m * m * m * m < n) m++; for (int c = 1; c < 100; c++) { long x = 0, y = 2, ys = 0, r = 1, q = 1, g = 1; while (g == 1) { x = y; for (int i = 0; i < r; i++) y = (y * y + c) % n; long k = 0; while (k < r && g == 1) { ys = y; for (int i = 0; i < m && i < r - k; i++) { y = (y * y + c) % n; q = q * Math.Abs(x - y) % n; } g = Gcd(q, n); k += m; } r <<= 1; } if (g == n) { g = 1; while (g == 1) { ys = (ys * ys + c) % n; g = Gcd(Math.Abs(x - ys), n); } } if (g < n) { if (IsPrimeMR(g)) return g; else if (IsPrimeMR(n / g)) return n / g; return FindFactorRho(g); } } return 1; } SortedDictionary PrimeFactoring(long n) { long i = 2; var ret = new SortedDictionary(); while (i * i <= n) { long k = 0; while (n % i == 0) { n /= i; k++; } if (k > 0) ret.Add(i, k); i += 1 + (i & 1); if (i == 101 && n >= (1 << 20)) { while (n > 1) { if (IsPrimeMR(n)) { ret.Add(n, 1); n = 1; } else { long j = FindFactorRho(n); k = 0; while (n % j == 0) { n /= j; k++; } ret.Add(j, k); } } } } if (n > 1) ret.Add(n, 1); return ret; } const long inf = (long)1 << 60; int ri { get { return (int)sc.Integer(); } } long rl { get { return sc.Integer(); } } double rd { get { return sc.Double(); } } string rs { get { return sc.Scan(); } } public StreamScanner sc = new StreamScanner(Console.OpenStandardInput()); void WriteJoin(string s, T[] t) { Console.WriteLine(string.Join(s, t)); } void WriteJoin(string s, List t) { Console.WriteLine(string.Join(s, t)); } void Write(T t) { Console.WriteLine(t.ToString()); } void Debug(T t) { Console.WriteLine(t.ToString()); Console.Out.Flush(); } void YN(bool t) { Console.WriteLine(t ? "YES" : "NO"); } void Yn(bool t) { Console.WriteLine(t ? "Yes" : "No"); } void yn(bool t) { Console.WriteLine(t ? "yes" : "no"); } } public static class Functions { public static int Popcount(long x) { x = x - ((x >> 1) & 0x5555555555555555); x = (x & 0x3333333333333333) + ((x >> 2) & 0x3333333333333333); x = (x + (x >> 4)) & 0x0f0f0f0f0f0f0f0f; x = x + (x >> 8); x = x + (x >> 16); x = x + (x >> 32); return (int)(x & 0x0000007f); } public static int Ctz(long x) { if (x == 0) return -1; return Popcount((x & -x) - 1); } public static int SafeMod(int x, int m) { int r = x % m; return r < 0 ? r + m : r; } public static long SafeMod(long x, long m) { long r = x % m; return r < 0 ? r + m : r; } public static long Floor(long a, long b) => a >= 0 ? a / b : (a + 1) / b - 1; public static long Ceil(long a, long b) => a > 0 ? (a - 1) / b + 1 : a / b; public static int Gcd(int a, int b) => b == 0 ? a : Gcd(b, a % b); public static long Gcd(long a, long b) => b == 0 ? a : Gcd(b, a % b); public static void Swap(ref int x, ref int y) { x ^= y; y ^= x; x ^= y; } public static void Swap(ref long x, ref long y) { x ^= y; y ^= x; x ^= y; } public static void Swap(ref T x, ref T y) { T t = y; y = x; x = t; } public static void Chmin(ref int x, int y) => x = Math.Min(x, y); public static void Chmin(ref long x, long y) => x = Math.Min(x, y); public static void Chmin(ref double x, double y) => x = Math.Min(x, y); public static void Chmax(ref int x, int y) => x = Math.Max(x, y); public static void Chmax(ref long x, long y) => x = Math.Max(x, y); public static void Chmax(ref double x, double y) => x = Math.Max(x, y); public static int LowerBound(in List list, S val, Func comp) { if (list.Count == 0) return -1; if (comp(list.Last(), val) <= 0) return list.Count; int l = 0, r = list.Count; while (l < r) { int x = (l + r) / 2; if (comp(list[x], val) < 0) l = x + 1; else r = x; } return l; } public static int UpperBound(in List list, S val, Func comp) { if (list.Count == 0) return 0; if (comp(list.Last(), val) < 0) return list.Count; int l = 0, r = list.Count; while (l < r) { int x = (l + r) / 2; if (comp(list[x], val) <= 0) l = x + 1; else r = x; } return l; } } public class StreamScanner { public StreamScanner(Stream stream) { str = stream; } private readonly Stream str; private readonly byte[] buf = new byte[1024]; private int len, ptr; public bool isEof = false; public bool IsEndOfStream { get { return isEof; } } private byte read() { if (isEof) throw new EndOfStreamException(); if (ptr >= len) { ptr = 0; if ((len = str.Read(buf, 0, 1024)) <= 0) { isEof = true; return 0; } } return buf[ptr++]; } public char Char() { byte b = 0; do b = read(); while (b < 33 || 126 < b); return (char)b; } public string Scan() { var sb = new StringBuilder(); for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b); return sb.ToString(); } public long Integer() { long ret = 0; byte b = 0; var ng = false; do b = read(); while (b != '-' && (b < '0' || '9' < b)); if (b == '-') { ng = true; b = read(); } for (; true; b = read()) { if (b < '0' || '9' < b) return ng ? -ret : ret; else ret = ret * 10 + b - '0'; } } public double Double() { return double.Parse(Scan()); } }