#pragma warning disable

using System;
using System.IO;
using System.Linq;
using System.Collections.Generic;
using System.Runtime.CompilerServices;
using static System.Console;
using static System.Math;
using static Util;
using System.Diagnostics;

#region using(AtCoder等非対応)
// using pii = (int, int);
// using pll = (long, long);
// using pdd = (double, double);
// using pss = (string, string);
// using pis = (int, string);
// using psi = (string, int);
// using pls = (long, string);
// using psl = (string, long);
// using pds = (double, string);
// using psd = (string, double);
// using pid = (int, double);
// using pdi = (double, int);
// using pld = (long, double);
// using pdl = (double, long);
// using vb = bool[];
// using vvb = bool[][];
// using vvvb = bool[][][];
// using vi = int[];
// using vvi = int[][];
// using vvvi = int[][][];
// using vl = long[];
// using vvl = long[][];
// using vvvl = long[][][];
// using vd = double[];
// using vvd = double[][];
// using vvvd = double[][][];
// using vs = string[];
// using vvs = string[][];
// using vvvs = string[][][];
// using listb = System.Collections.Generic.List<bool>;
// using llistb = System.Collections.Generic.List<System.Collections.Generic.List<bool>>;
// using lllistb = System.Collections.Generic.List<System.Collections.Generic.List<System.Collections.Generic.List<bool>>>;
// using listi = System.Collections.Generic.List<int>;
// using llisti = System.Collections.Generic.List<System.Collections.Generic.List<int>>;
// using lllisti = System.Collections.Generic.List<System.Collections.Generic.List<System.Collections.Generic.List<int>>>;
// using listl = System.Collections.Generic.List<long>;
// using llistl = System.Collections.Generic.List<System.Collections.Generic.List<long>>;
// using lllistl = System.Collections.Generic.List<System.Collections.Generic.List<System.Collections.Generic.List<long>>>;
// using listd = System.Collections.Generic.List<double>;
// using llistd = System.Collections.Generic.List<System.Collections.Generic.List<double>>;
// using lllistd = System.Collections.Generic.List<System.Collections.Generic.List<System.Collections.Generic.List<double>>>;
// using lists = System.Collections.Generic.List<string>;
// using llists = System.Collections.Generic.List<System.Collections.Generic.List<string>>;
// using lllists = System.Collections.Generic.List<System.Collections.Generic.List<System.Collections.Generic.List<string>>>;
// using mii = System.Collections.Generic.SortedDictionary<int, int>;
// using mll = System.Collections.Generic.SortedDictionary<long, long>;
// using mss = System.Collections.Generic.SortedDictionary<string, string>;
// using mis = System.Collections.Generic.SortedDictionary<int, string>;
// using msi = System.Collections.Generic.SortedDictionary<string, int>;
// using mls = System.Collections.Generic.SortedDictionary<long, string>;
// using msl = System.Collections.Generic.SortedDictionary<string, long>;
// using umii = System.Collections.Generic.Dictionary<int, int>;
// using umll = System.Collections.Generic.Dictionary<long, long>;
// using umss = System.Collections.Generic.Dictionary<string, string>;
// using umis = System.Collections.Generic.Dictionary<int, string>;
// using umsi = System.Collections.Generic.Dictionary<string, int>;
// using umls = System.Collections.Generic.Dictionary<long, string>;
// using umsl = System.Collections.Generic.Dictionary<string, long>;
// using seti = System.Collections.Generic.SortedSet<int>;
// using setl = System.Collections.Generic.SortedSet<long>;
// using sets = System.Collections.Generic.SortedSet<string>;
// using useti = System.Collections.Generic.HashSet<int>;
// using usetl = System.Collections.Generic.HashSet<long>;
// using usets = System.Collections.Generic.HashSet<string>;
#endregion


class Util {
	public static double PI = 3.141592653589793;
	public static long m107 = 1000000007;
	public static long m998 = 998244353;
	public static int a10_9 = 1000000000;
	public static long a10_18 = 1000000000000000000;
	public static int iinf = 1 << 30;
	public static long linf = (1l << 61) - (1l << 31);

	/// <summary>1行読みこみ</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static string read() => ReadLine();

	/// <summary>1行読みこみ</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static string readln() => ReadLine();

	/// <summary>1行読みこみ</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static string readline() => ReadLine();

	/// <summary>改行なし出力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void write() => Write("");

	/// <summary>改行なし出力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void write<T>(T value) => Write(value);

	/// <summary>改行あり出力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void writeln() => WriteLine("");

	/// <summary>改行あり出力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void writeln<T>(T value) => WriteLine(value);

	/// <summary>改行あり出力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void writeline() => WriteLine("");

	/// <summary>改行あり出力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void writeline<T>(T value) => WriteLine(value);

	/// <summary>改行なし出力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void print() => Write("");

	/// <summary>改行なし出力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void print<T>(T value) => Write(value);

	/// <summary>改行あり出力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void println() => WriteLine("");

	/// <summary>改行あり出力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void println<T>(T value) => WriteLine(value);

	/// <summary>改行あり出力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void printline() => WriteLine("");

	/// <summary>改行あり出力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void printline<T>(T value) => WriteLine(value);

	/// <summary>任意の要素数・初期値の配列を作って初期化する</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static T[] makearr<T>(int num, T value) {
		var arr = new T[num];
		for (int i = 0; i < num; ++i) arr[i] = value;
		return arr;
	} // end of func

	/// <summary>任意の要素数・初期値の２次元配列を作って初期化する</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static T[][] makearr2<T>(int height, int width, T value) {
		var arr = new T[height][];
		for (int i = 0; i < height; ++i) {
			arr[i] = new T[width];
			for (int j = 0; j < width; ++j) {
				arr[i][j] = value;
			}
		}
		return arr;
	} // end of func

	/// <summary>任意の要素数・初期値の3次元配列を作って初期化する</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static T[][][] makearr3<T>(int height, int width, int depth, T value) {
		var arr = new T[height][][];
		for (int i = 0; i < height; ++i) {
			arr[i] = new T[width][];
			for (int j = 0; j < width; ++j) {
				arr[i][j] = new T[depth];
				for (int k = 0; k < depth; ++k) {
					arr[i][j][k] = value;
				}
			}
		}
		return arr;
	} // end of func

	/// <summary>任意の要素数・初期値のListを作って初期化する</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static List<T> makelist<T>(int num, T value) {
		return new List<T>(makearr(num, value));
	} // end of func

	/// <summary>任意の要素数・初期値の2次元Listを作って初期化する</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static List<List<T>> makelist2<T>(int height, int width, T value) {
		var arr = new List<List<T>>();
		for (int i = 0; i < height; ++i) {
			arr.Add(makelist(width, value));
		}
		return arr;
	} // end of func

	/// <summary>任意の要素数・初期値の3次元Listを作って初期化する</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static List<List<List<T>>> makelist3<T>(int height, int width, int depth, T value) {
		var arr = new List<List<List<T>>>();
		for (int i = 0; i < height; ++i) {
			arr[i] = new List<List<T>>();
			for (int j = 0; j < width; ++j) {
				arr[i].Add(makelist(depth, value));
			}
		}
		return arr;
	} // end of func

	/// <summary>1次元配列のディープコピーを行う</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static T[] copyarr<T>(T[] arr) {
		T[] brr = new T[arr.Length];
		Array.Copy(arr, brr, arr.Length);
		return brr;
	} // end of func 

	/// <summary>2次元配列のディープコピーを行う</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static T[][] copyarr2<T>(T[][] arr) {
		T[][] brr = new T[arr.Length][];
		for (int i = 0; i < arr.Length; ++i) {
			brr[i] = new T[arr[i].Length];
			Array.Copy(arr[i], brr[i], arr[i].Length);
		}
		return brr;
	} // end of func

	/// <summary>3次元配列のディープコピーを行う</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static T[][][] copyarr3<T>(T[][][] arr) {
		T[][][] brr = new T[arr.Length][][];
		for (int i = 0; i < arr.Length; ++i) {
			brr[i] = new T[arr[i].Length][];
			for (int j = 0; j < arr[i].Length; ++j) {
				brr[i][j] = new T[arr[i][j].Length];
				Array.Copy(arr[i][j], brr[i][j], arr[i][j].Length);
			}
		}
		return brr;
	} // end of func

	/// <summary>1次元Listのディープコピーを行う</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static List<T> copylist<T>(List<T> list) {
		return new List<T>(list);
	} // end of func

	/// <summary>2次元Listのディープコピーを行う</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static List<List<T>> copylist2<T>(List<List<T>> list) {
		List<List<T>> list2 = new List<List<T>>();
		for (int i = 0; i < list.Count; ++i) {
			list2.Add(new List<T>(list[i]));
		}
		return list2;
	} // end of func

	/// <summary>3次元Listのディープコピーを行う</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static List<List<List<T>>> copylist3<T>(List<List<List<T>>> list) {
		List<List<List<T>>> list2 = new List<List<List<T>>>();
		for (int i = 0; i < list.Count; ++i) {
			List<List<T>> tmplist = new List<List<T>>();
			for (int j = 0; j < list[i].Count; ++i) {
				tmplist.Add(new List<T>(list[i][j]));
			}
			list2.Add(tmplist);
		}
		return list2;
	} // end of func

	/// <summary>1次元Listを出力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void printlist<T>(List<T> list) {
		WriteLine(string.Join(" ", list));
	} // end of func

	/// <summary>1次元配列を出力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void printlist<T>(T[] list) {
		WriteLine(string.Join(" ", list));
	} // end of func

	/// <summary>2次元リストを出力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void printlist2<T>(List<List<T>> list) {
		foreach (var l in list) {
			WriteLine(string.Join(" ", l));
		}
	} // end of func

	/// <summary>2次元配列を出力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void printlist2<T>(T[][] list) {
		foreach (var l in list) {
			WriteLine(string.Join(" ", l));
		}
	} // end of func	

	/// <summary>1次元Listを出力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void printarr<T>(List<T> list) {
		WriteLine(string.Join(" ", list));
	} // end of func

	/// <summary>1次元配列を出力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void printarr<T>(T[] list) {
		WriteLine(string.Join(" ", list));
	} // end of func

	/// <summary>2次元リストを出力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void printarr2<T>(List<List<T>> list) {
		foreach (var l in list) {
			WriteLine(string.Join(" ", l));
		}
	} // end of func

	/// <summary>2次元配列を出力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void printarr2<T>(T[][] list) {
		foreach (var l in list) {
			WriteLine(string.Join(" ", l));
		}
	} // end of func

	/// <summary>ジェネリックを出力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void printiter<T>(IEnumerable<T> generic) {
		foreach (var it in generic) {
			Write(it + " ");
		}
		WriteLine();
	} // end of func

	/// <summary>ジェネリックを出力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void printlineiter<T>(IEnumerable<T> generic) {
		foreach (var it in generic) {
			WriteLine(it + " ");
		}
	} // end of func

	/// <summary>数字を1つint型で読み込み</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static int readint() {
		return int.Parse(ReadLine());
	} // end of func

	/// <summary>数字を1つlong型で読み込み</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static long readlong() {
		return long.Parse(ReadLine());
	} // end of func

	/// <summary>入力を空白区切りのstringで返す(変則的な入力に対応)</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static string[] readsplit() {
		return ReadLine().Split(' ');
	} // end of func

	/// <summary>数字をスペース区切りでint型で入力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static int[] readints() {
		return ReadLine().Split(' ').Select(_ => int.Parse(_)).ToArray();
	} // end of func

	/// <summary>数字をスペース区切りでlong型で入力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static long[] readlongs() {
		return ReadLine().Split(' ').Select(_ => long.Parse(_)).ToArray();
	} // end of func

	/// <summary>数字をスペース区切りでfloat型で入力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static float[] readfloats() {
		return ReadLine().Split(' ').Select(_ => float.Parse(_)).ToArray();
	} // end of func

	/// <summary>数字をスペース区切りでdouble型で入力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static double[] readdoubles() {
		return ReadLine().Split(' ').Select(_ => double.Parse(_)).ToArray();
	} // end of func

	/// <summary>文字列をスペース区切りで入力</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static string[] readstrings() {
		return ReadLine().Split(' ');
	} // end of func

	/// <summary>読み込んだint2つをタプルで返す(分解代入用)</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static (int, int) readintt2() {
		var arr = readints();
		return (arr[0], arr[1]);
	} // end of func

	/// <summary>読み込んだint3つをタプルで返す(分解代入用)</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static (int, int, int) readintt3() {
		var arr = readints();
		return (arr[0], arr[1], arr[2]);
	} // end of func

	/// <summary>読み込んだint4つをタプルで返す(分解代入用)</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static (int, int, int, int) readintt4() {
		var arr = readints();
		return (arr[0], arr[1], arr[2], arr[3]);
	} // end of func

	/// <summary>読み込んだlong2つをタプルで返す(分解代入用)</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static (long, long) readlongt2() {
		var arr = readlongs();
		return (arr[0], arr[1]);
	} // end of func

	/// <summary>読み込んだ数long3つをタプルで返す(分解代入用)</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static (long, long, long) readlongt3() {
		var arr = readlongs();
		return (arr[0], arr[1], arr[2]);
	} // end of func

	/// <summary>読み込んだ数long4つをタプルで返す(分解代入用)</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static (long, long, long, long) readlongt4() {
		var arr = readlongs();
		return (arr[0], arr[1], arr[2], arr[3]);
	} // end of func

	/// <summary>読み込んだfloat2つをタプルで返す(分解代入用)</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static (float, float) readfloatt2() {
		var arr = readfloats();
		return (arr[0], arr[1]);
	} // end of func

	/// <summary>読み込んだfloat3つをタプルで返す(分解代入用)</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static (float, float, float) readfloatt3() {
		var arr = readfloats();
		return (arr[0], arr[1], arr[2]);
	} // end of func

	/// <summary>読み込んだfloat4つをタプルで返す(分解代入用)</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static (float, float, float, float) readfloatt4() {
		var arr = readfloats();
		return (arr[0], arr[1], arr[2], arr[3]);
	} // end of func

	/// <summary>読み込んだdouble2つをタプルで返す(分解代入用)</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static (double, double) readdoublet2() {
		var arr = readdoubles();
		return (arr[0], arr[1]);
	} // end of func

	/// <summary>読み込んだdouble3つをタプルで返す(分解代入用)</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static (double, double, double) readdoublet3() {
		var arr = readdoubles();
		return (arr[0], arr[1], arr[2]);
	} // end of func

	/// <summary>読み込んだdouble4つをタプルで返す(分解代入用)</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static (double, double, double, double) readdoublet4() {
		var arr = readdoubles();
		return (arr[0], arr[1], arr[2], arr[3]);
	} // end of func

	/// <summary>読み込んだstring2つをタプルで返す(分解代入用)</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static (string, string) readstringt2() {
		var arr = ReadLine().Split(' ');
		return (arr[0], arr[1]);
	} // end of func

	/// <summary>読み込んだstring3つをタプルで返す(分解代入用)</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static (string, string, string) readstringt3() {
		var arr = ReadLine().Split(' ');
		return (arr[0], arr[1], arr[2]);
	} // end of func

	/// <summary>読み込んだstring3つをタプルで返す(分解代入用)</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static (string, string, string, string) readstringt4() {
		var arr = ReadLine().Split(' ');
		return (arr[0], arr[1], arr[2], arr[3]);
	} // end of func

	/// <summary>先頭に要素数(int)と次にでかい数字1つ</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static (int, long) readintlongt2() {
		var arr = ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
		return ((int)arr[0], arr[1]);
	} // end of func

	/// <summary>先頭に要素数(int)と次にでかい数字2つ</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static (int, long, long) readintlongt3() {
		var arr = ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
		return ((int)arr[0], arr[1], arr[2]);
	} // end of func

	/// <summary>先頭に要素数(int)と次にでかい数字2つ</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static (int, long, long, long) readintlongt4() {
		var arr = ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
		return ((int)arr[0], arr[1], arr[2], arr[3]);
	} // end of func

	/// <summary>小数点以下を16桁で表示(精度が厳しい問題に対応)</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void WriteLine16<T>(T num) {
		WriteLine(string.Format("{0:0.################}", num));
	} // end of func

	/// <summary>整数を二進数で表示</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void WriteLine2bit(int num) {
		WriteLine(Convert.ToString(num, 2));
	} // end of func

	/// <summary>整数を二進数で表示</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void WriteLine2bit(long num) {
		WriteLine(Convert.ToString(num, 2));
	} // end of func

	/// <summary>整数を2進数表現した文字列に</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static string IntToString2bit(int num) {
		return Convert.ToString(num, 2);
	} // end of func

	/// <summary>整数を2進数表現した文字列に</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static string LongToString2bit(long num) {
		return Convert.ToString(num, 2);
	} // end of func

	/// <summary>出力のflush削除</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void preprocess() {
		var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
		System.Console.SetOut(sw);
	} // end of func

	/// <summary>出力をflush</summary>
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public static void finalprocess() {
		System.Console.Out.Flush();
	} // end of func
} // end of class

/// 座標に便利(値型だけど16byteまではstructが速い)
struct YX {
	public int y;
	public int x;
	public YX(int y, int x) {
		this.y = y;
		this.x = x;
	}
} // end of class

/// グラフをするときに(値型だけど16byteまではstructが速い)
struct Edge {
	public int from;
	public int to;
	public long cost;
	public Edge(int from, int to, long cost) {
		this.from = from;
		this.to = to;
		this.cost = cost;
	}
} // end of class

class Kyopuro {
	public static void Main() {
		preprocess();
		var kyopuro = new Kyopuro();
		kyopuro.Solve();
		finalprocess();
	} // end of func


	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public bool IsPrime(long num) {
		if (num == 2) return true;
		// 2未満の数と偶数は素数ではない
		if (num < 2l || num % 2l == 0) return false;

		// n - 1 = 2^s * d と表す
		long s = 0;
		long d = num - 1;
		while (d % 2l == 0) {
			++s;
			d /= 2l;
		}


		// var rand = new long[] { 2, 325, 9375, 28178, 450775, 9780504, 1795265022 };
		// foreach (var r in rand) {
		var rand = new Random();
		for (int i = 0; i < 10; ++i) {
			long r = rand.NextInt64(2, num - 1);
			long x = KurikaeshiPow(r, d, num);
			if (x == 1l || x == num - 1l) continue;

			for (long j = 0; j < s - 1l; ++j) {
				x = KurikaeshiPow(x, 2, num);
				if (x == 1l) return false;
				if (x == num - 1) break;
			}
			if (x != num - 1) return false;
		}

		return true;
	}


	// a^b mod n を計算する関数
	public static long ModPow(long a, long b, long n) {
		long result = 1;
		a %= n;
		while (b > 0) {
			if (b % 2 == 1)
				result = (result * a) % n;
			b /= 2;
			a = (a * a) % n;
		}
		return result;
	}


	/// a^nを繰り返し二乗法
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public long KurikaeshiPow(long a, long n, long mod = long.MaxValue) {
		if (n == 0) return 1;
		if (n == 1) return a % mod;

		long ret = 1;
		while (n > 0) {
			// a^(2^k) をかけていく k = nを二進数表現したときに1が立っているbit
			if ((n & 1) == 1) ret = (ret * a) % mod;
			n >>= 1;
			a = (a * a) % mod;
		}

		return ret;
	} // end of method

	public void Solve() {

		// writeline(IsPrime(2));
		// return;

		// var sw = new Stopwatch();
		// sw.Start();

		long lmax = 100000l;
		var prr = new List<long>(new long[1] { 2 });
		var arr = new bool[lmax + 1];
		for (int i = 2; i <= lmax; i += 2) arr[i] = false;
		for (int i = 3; i <= lmax; i += 2) {
			if (arr[i]) continue;
			prr.Add(i);
			int ii = i;
			while (ii <= lmax) {
				arr[ii] = true;
				ii += i;
			}
		}

		// sw.Stop();
		// writeline(sw.Elapsed);
		// return;

		int q = readint();
		for (int i = 0; i < q; ++i) {
			long a = readlong();
			foreach (long p in prr) {
				if (a % p != 0) continue;
				a /= p;
				break;
			}
			if (a == 1) {
				writeline("No");
				continue;
			}

			foreach (long p in prr) {
				if (a % p != 0) continue;
				a /= p;
				break;
			}
			if (a == 1) {
				writeline("No");
				continue;
			}


			writeline(IsPrime(a) ? "Yes" : "No");
		}



	} // end of method
} // end of class