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; if (n <= 1) return false; long d = n - 1; while ((d & 1) == 0) d >>= 1; var aarr = new long[] { 2, 325, 9375, 28178, 450775, 9780504, 1795265022 }; var mont = new Montgomery(n); foreach (var a in aarr) { if (n <= a) break; long t = d, x = a, y = 1; while (t > 0) { if ((t & 1) == 1) y = mont.Mul(x, y); x = mont.Mul(x, x); t >>= 1; } t = d; while (t != n - 1 && y != 1 && y != n - 1) { y = mont.Mul(y, y); t <<= 1; } if (y != n - 1 && (t & 1) == 0) return false; } return true; } long FindFactorRho(long n) { var mont = new Montgomery(n); long m = 1; while (m * m * m * m * m * m * m * m < n) m++; for (int c = 1; c < 10000; c++) { long x = 1, y = c, ys = 0, q = 1; long g = 1; for (int r = 1; g == 1; r <<= 1) { x = y; for (int i = 0; i < r; ++i) y = mont.Conv(mont.Mul(y, y) + c); for (long k = 0; g == 1 && k < r; k += m) { ys = y; for (int i = 0; i < m && i < r - k; ++i) { y = mont.Conv(mont.Mul(y, y) + c); q = mont.Mul(q, Math.Abs(x - y)); } g = Math.Abs(Gcd(q, n)); } } if (g == n) { do { ys = mont.Conv(mont.Mul(ys, ys) + c); g = Gcd(Math.Abs(x - ys), n); } while (g == 1); } if (g != n) return g; } return n; } 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; } class Montgomery { long n, nr, mask; UInt128 r2; int nb; public Montgomery(long _n) { n = _n; nb = 0; while (n >= (1L << nb)) nb++; r2 = ((UInt128)1 << (nb * 2)) % n; mask = (1L << nb) - 1; nr = 0; long t = 0, vi = 1; for (int i = 0; i < nb; i++) { if ((t & 1) == 0) { t += n; nr += vi; } t >>= 1; vi <<= 1; } } public long Reduction(UInt128 t) { UInt128 c = t * nr; c &= mask; c *= n; c += t; c >>= nb; if (c >= n) c -= n; return c; } public long Conv(UInt128 a) => Reduction(Reduction(a) * r2); public long Mul(UInt128 a, UInt128 b) => Reduction(Reduction(a * b) * r2); public long Pow(UInt128 a, long b) { long p = Reduction(a * r2); long x = Reduction(r2); long y = b; while (y > 0) { if ((y & 1) == 1) x = Reduction(x * p); p = Reduction(p * p); y >>= 1; } return Reduction(x); } } struct UInt128 { private const int l = 64; private const ulong MaxValue = ulong.MaxValue; public ulong t, b; public UInt128(long n) : this(0, (ulong)n) { } public UInt128(ulong n) : this(0, n) { } public UInt128(long _t, long _b) : this((ulong)_t, (ulong)_b) { } public UInt128(ulong _t, ulong _b) { t = _t; b = _b; } public static implicit operator UInt128(int n) => new UInt128(n); public static implicit operator UInt128(long n) => new UInt128(n); public static implicit operator UInt128(ulong n) => new UInt128(n); public static implicit operator ulong(UInt128 n) => n.b; public static implicit operator long(UInt128 n) => (long)n.b; public override bool Equals(object obj) { if (obj == null || GetType() != obj.GetType()) return false; var x = (UInt128)obj; return x.t == t && x.b == b; } public override int GetHashCode() => t.GetHashCode() ^ b.GetHashCode(); public override string ToString() => $"UInt128({t},{b})"; public static bool operator ==(UInt128 x, UInt128 y) => Equals(x, y); public static bool operator !=(UInt128 x, UInt128 y) => !Equals(x, y); public static bool operator <(UInt128 x, UInt128 y) => x.t != y.t ? x.t < y.t : x.b < y.b; public static bool operator >(UInt128 x, UInt128 y) => x.t != y.t ? x.t > y.t : x.b > y.b; public static bool operator <=(UInt128 x, UInt128 y) => x.t != y.t ? x.t < y.t : x.b <= y.b; public static bool operator >=(UInt128 x, UInt128 y) => x.t != y.t ? x.t > y.t : x.b >= y.b; public static UInt128 operator +(UInt128 x, UInt128 y) => x.b <= MaxValue - y.b ? new UInt128(x.t + y.t, x.b + y.b) : new UInt128(x.t + y.t + 1, x.b + y.b); public static UInt128 operator -(UInt128 x, UInt128 y) => x.b >= y.b ? new UInt128(x.t - y.t, x.b - y.b) : new UInt128(x.t - y.t - 1, x.b + (MaxValue - y.b) + 1); public static UInt128 operator *(UInt128 x, UInt128 y) { const ulong mask = (1UL << (l / 4)) - 1; var p = new ulong[8]; var q = new ulong[8]; for (int i = 0; i < 4; i++) { p[i] = (x.b >> (l / 4 * i)) & mask; p[i + 4] = (x.t >> (l / 4 * i)) & mask; q[i] = (y.b >> (l / 4 * i)) & mask; q[i + 4] = (y.t >> (l / 4 * i)) & mask; } var r = new ulong[8]; for (int i = 0; i < 8; i++) for (int j = 0; i + j < 8; j++) r[i + j] += p[i] * q[j]; for (int i = 0; i < 7; i++) r[i + 1] += r[i] >> (l / 4); for (int i = 0; i < 8; i++) r[i] &= mask; ulong t = 0, b = 0; for (int i = 0; i < 4; i++) { b |= r[i] << (l / 4 * i); t |= r[i + 4] << (l / 4 * i); } return new UInt128(t, b); } public static UInt128 operator /(UInt128 x, UInt128 y) { ulong a = (ulong)1 << (l - 1), b = 0; var t = y >> 1; while (t > 0) { if (a == 1) { a = 0; b = (ulong)1 << (l - 1); } else if (a > 0) a >>= 1; else b >>= 1; t >>= 1; } const ulong mask = (1UL << (l / 4)) - 1; ulong[] p, q, r; ulong aprv = a, bprv = b; while (true) { p = new ulong[16]; q = new ulong[16]; for (int i = 0; i < 4; i++) { p[i] = (y.b >> (l / 4 * i)) & mask; p[i + 4] = (y.t >> (l / 4 * i)) & mask; q[i] = (b >> (l / 4 * i)) & mask; q[i + 4] = (a >> (l / 4 * i)) & mask; } r = new ulong[16]; for (int i = 0; i < 16; i++) for (int j = 0; i + j < 16; j++) r[i + j] += p[i] * q[j]; for (int j = 0; j < 15; j++) { r[j + 1] += r[j] >> (l / 4); r[j] &= mask; } for (int i = 0; i < 8; i++) p[i] = mask - r[i]; for (int i = 0; i < 8; i++) { if (p[i] != mask) { p[i]++; break; } else p[i] = 0; } p[8]++; r = new ulong[16]; for (int i = 0; i < 16; i++) for (int j = 0; i + j < 16; j++) r[i + j] += p[i] * q[j]; for (int i = 0; i < 15; i++) { r[i + 1] += r[i] >> (l / 4); r[i] &= mask; } a = 0; b = 0; for (int i = 0; i < 4; i++) { a |= r[i + 12] << (l / 4 * i); b |= r[i + 8] << (l / 4 * i); } if (a == aprv && b == bprv) break; aprv = a; bprv = b; } p = new ulong[16]; q = new ulong[16]; for (int j = 0; j < 4; j++) { p[j] = (x.b >> (l / 4 * j)) & mask; p[j + 4] = (x.t >> (l / 4 * j)) & mask; q[j] = (b >> (l / 4 * j)) & mask; q[j + 4] = (a >> (l / 4 * j)) & mask; } r = new ulong[16]; for (int j = 0; j < 8; j++) for (int k = 0; k < 8; k++) r[j + k] += q[j] * p[k]; for (int j = 0; j < 15; j++) { r[j + 1] += r[j] >> (l / 4); r[j] &= mask; } a = 0; b = 0; for (int j = 0; j < 4; j++) { a |= r[j + 12] << (l / 4 * j); b |= r[j + 8] << (l / 4 * j); } var n = new UInt128(a, b); return x >= y * (n + 1) ? n + 1 : n; } public static UInt128 operator %(UInt128 x, UInt128 y) => x - (x / y) * y; public static UInt128 operator >>(UInt128 x, int d) { if (d >= 2 * l) return new UInt128(0); if (d >= l) return new UInt128(0, x.t >> (d - l)); return new UInt128(x.t >> d, ((x.t ^ ((x.t >> d) << d)) << (l - d)) | (x.b >> d)); } public static UInt128 operator <<(UInt128 x, int d) { if (d >= 2 * l) return new UInt128(0); if (d >= l) return new UInt128(x.b << (d - l), 0); return new UInt128((x.t << d) | ((x.b ^ ((x.b << d) >> d)) >> (l - d)), x.b << d); } public static UInt128 operator &(UInt128 x, UInt128 y) => new UInt128(x.t & y.t, x.b & y.b); public static UInt128 operator |(UInt128 x, UInt128 y) => new UInt128(x.t | y.t, x.b | y.b); } 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()); } }