/+ dub.sdl: name "A" dependency "dcomp" version=">=0.7.3" +/ import std.stdio, std.algorithm, std.range, std.conv; // import dcomp.foundation, dcomp.scanner; T pow_mod(T)(T x, long n, T md) { T r = 1; while (n) { if (n & 1) r = (r*x)%md; x = (x*x)%md; n >>= 1; } return r % md; } // import dcomp.bigint; bool isPrime(long n) { if (n <= 1) return false; if (n == 2) return true; if (n % 2 == 0) return false; alias Int = uintN!2; long d = n-1; while (d % 2 == 0) d /= 2; long[] alist = [2,3,5,7,11,13,17,19,23,29,31,37]; foreach (a; alist) { if (n <= a) break; long t = d; Int y = pow_mod!Int(Int(a), t, Int(n)); while (t != n-1 && y != Int(1) && y != Int(n-1)) { y = y*y % Int(n); t <<= 1; } if (y != Int(n-1) && t % 2 == 0) { return false; } } return true; } bool ck2(long x) { import std.math; if (isPrime(x)) return true; foreach (i; 2..100) { long y = cast(long)(pow(x, 1.0/i) + 0.001); if (!isPrime(y)) continue; long z = 1; foreach (j; 0..i) z *= y; if (z == x) return true; } return false; } bool solve(long x) { if (x == 2) return false; if (x % 2 == 0) return true; long b = 2; while (b < x) { if (ck2(x-b)) return true; b *= 2; } return false; } int main() { Scanner sc = new Scanner(stdin); // Scanner sc = new Scanner(File("tests/Ain0.txt")); int q; sc.read(q); foreach (i; 0..q) { long x; sc.read(x); if (solve(x)) writeln("Yes"); else writeln("No"); } return 0; } /* IMPORT /Users/yosupo/Program/dcomp/source/dcomp/bigint.d */ // module dcomp.bigint; import core.checkedint, core.bitop; // import dcomp.int128, dcomp.foundation; void addMultiWord(in ulong[] l, in ulong[] r, ulong[] res) { auto N = res.length; bool of = false; foreach (i; 0..N) { bool nof; res[i] = addu( (i < l.length) ? l[i] : 0UL, (i < r.length) ? r[i] : 0UL, nof); if (of) { res[i]++; nof |= (res[i] == 0); } of = nof; } } void subMultiWord(in ulong[] l, in ulong[] r, ulong[] res) { auto N = res.length; bool of = false; foreach (i; 0..N) { bool nof; res[i] = subu( (i < l.length) ? l[i] : 0UL, (i < r.length) ? r[i] : 0UL, nof); if (of) { res[i]--; nof |= (res[i] == ulong.max); } of = nof; } } void mulMultiWord(in ulong[] l, in ulong r, ulong[] res) { auto N = res.length; ulong ca; foreach (i; 0..N) { auto u = mul128((i < l.length) ? l[i] : 0UL, r); bool of; res[i] = addu(u[0], ca, of); if (of) u[1]++; ca = u[1]; } } void shiftLeftMultiWord(in ulong[] l, int n, ulong[] res) { size_t N = res.length; int ws = n / 64; int bs = n % 64; import std.stdio; foreach_reverse (ptrdiff_t i; 0..N) { ulong b = (0 <= i-ws && i-ws < l.length) ? l[i-ws] : 0UL; if (bs == 0) res[i] = b; else { ulong a = (0 <= i-ws-1 && i-ws-1 < l.length) ? l[i-ws-1] : 0UL; res[i] = (b << bs) | (a >> (64-bs)); } } } int cmpMultiWord(in ulong[] l, in ulong[] r) { import std.algorithm : max; auto N = max(l.length, r.length); foreach_reverse (i; 0..N) { auto ld = (i < l.length) ? l[i] : 0UL; auto rd = (i < r.length) ? r[i] : 0UL; if (ld < rd) return -1; if (ld > rd) return 1; } return 0; } struct uintN(int N) if (N >= 1) { import core.checkedint; ulong[N] d; this(ulong x) { d[0] = x; } this(string s) { foreach (c; s) { this *= 10; this += uintN(c-'0'); } } string toString() { import std.algorithm : reverse; char[] s; if (!this) return "0"; while (this) { s ~= cast(char)('0' + (this % uintN(10))[0]); this /= uintN(10); } reverse(s); return s.idup; } ref inout(ulong) opIndex(int idx) inout { return d[idx]; } T opCast(T: bool)() { import std.algorithm, std.range; return d[].find!"a!=0".empty == false; } uintN opUnary(string op)() const if (op == "~") { uintN res; foreach (i; 0..N) { res[i] = ~d[i]; } return res; } uintN opBinary(string op)(in uintN r) const if (op == "&" || op == "|" || op == "^") { uintN res; foreach (i; 0..N) { res[i] = mixin("d[i]" ~ op ~ "r.d[i]"); } return res; } uintN opBinary(string op : "<<")(int n) const { if (N * 64 <= n) return uintN(0); uintN res; int ws = n / 64; int bs = n % 64; if (bs == 0) { res.d[ws..N][] = d[0..N-ws][]; return res; } foreach_reverse (i; 1..N-ws) { res[i+ws] = (d[i] << bs) | (d[i-1] >> (64-bs)); } res[ws] = (d[0] << bs); return res; } uintN opBinary(string op : ">>")(int n) const { if (N * 64 <= n) return uintN(0); uintN res; int ws = n / 64; int bs = n % 64; if (bs == 0) { res.d[0..N-ws][] = d[ws..N][]; return res; } foreach_reverse (i; 0..N-ws-1) { res[i] = (d[i+ws+1] >> (64-bs)) | (d[i+ws] << bs); } res[N-ws-1] = (d[N-1] << bs); return res; } int opCmp(in uintN r) const { return cmpMultiWord(d, r.d); } uintN opUnary(string op)() if (op == "++") { uintN res; bool of = true; foreach (i; 0..N) { if (of) { d[i]++; if (d[i]) of = false; } } return res; } uintN opUnary(string op)() if (op == "--") { return this -= uintN(1); } uintN opUnary(string op)() const if (op=="+" || op=="-") { if (op == "+") return this; if (op == "-") { return ++(~this); } } uintN opBinary(string op : "+")(in uintN r) const { uintN res; addMultiWord(d, r.d, res.d); return res; } uintN opBinary(string op : "-")(in uintN r) const { uintN res; subMultiWord(d, r.d, res.d); return res; } uintN opBinary(string op : "*")(in uintN r) const { uintN res; foreach (i; 0..N) { ulong carry = 0; foreach (j; 0..N-1-i) { int s = i+j; bool of; auto u = mul128(d[i], r[j]); res[s] = addu(res[s], carry, of); carry = u[1]; if (of) carry++; res[s] = addu(res[s], u[0], of); if (of) carry++; } res[N-1] += d[i] * r[N-1-i] + carry; } return res; } uintN opBinary(string op : "*")(in ulong r) const { uintN res; mulMultiWord(d, r, res.d); return res; } uintN opBinary(string op : "/")(ulong rr) const { import std.stdio; uintN res; ulong back = 0; foreach_reverse (i; 0..N) { assert(back < rr); ulong pred = div128([d[i], back], rr); res[i] = pred; back = d[i]-(rr*pred); } return res; } uintN opBinary(string op : "/")(in uintN rr) const { int up = -1, shift; foreach_reverse (i; 0..N) { if (rr[i]) { up = i; shift = 63 - bsr(rr[i]); break; } } assert(up != -1); if (up == 0) { return this / ulong(rr[0]); } ulong[N+1] l; l[0..N] = d[0..N]; shiftLeftMultiWord(l, shift, l); auto r = (rr << shift); uintN res; foreach_reverse (i; 0..N-up) { ulong pred = (r[up] == ulong.max) ? l[i+up+1] : div128([l[i+up], l[i+up+1]], r[up]+1); res[i] = pred; ulong[N+1] buf; mulMultiWord(r.d[], pred, buf); subMultiWord(l[i..i+up+2], buf[], l[i..i+up+2]); while (cmpMultiWord(l[i..i+up+2], r.d[]) != -1) { res[i]++; subMultiWord(l[i..i+up+2], r.d[], l[i..i+up+2]); } } return res; } uintN opBinary(string op : "/")(in ulong r) const { return this / uintN(r); } uintN opBinary(string op : "%", T)(in T r) const { return this - this/r*r; } auto opOpAssign(string op, T)(in T r) { return mixin("this=this" ~ op ~ "r"); } } /* IMPORT /Users/yosupo/Program/dcomp/source/dcomp/array.d */ // module dcomp.array; T[N] fixed(T, size_t N)(T[N] a) {return a;} struct FastAppender(A, size_t MIN = 4) { import std.algorithm : max; import std.conv; import std.range.primitives : ElementEncodingType; import core.stdc.string : memcpy; private alias T = ElementEncodingType!A; private T* _data; private uint len, cap; @property size_t length() const {return len;} bool empty() const { return len == 0; } void reserve(size_t nlen) { import core.memory : GC; if (nlen <= cap) return; void* nx = GC.malloc(nlen * T.sizeof); cap = nlen.to!uint; if (len) memcpy(nx, _data, len * T.sizeof); _data = cast(T*)(nx); } void free() { import core.memory : GC; GC.free(_data); } void opOpAssign(string op : "~")(T item) { if (len == cap) { reserve(max(MIN, cap*2)); } _data[len++] = item; } void insertBack(T item) { this ~= item; } void removeBack() { len--; } void clear() { len = 0; } ref inout(T) back() inout { assert(len); return _data[len-1]; } ref inout(T) opIndex(size_t i) inout { return _data[i]; } T[] data() { return (_data) ? _data[0..len] : null; } } /* IMPORT /Users/yosupo/Program/dcomp/source/dcomp/scanner.d */ // module dcomp.scanner; // import dcomp.array; class Scanner { import std.stdio : File; import std.conv : to; import std.range : front, popFront, array, ElementType; import std.array : split; import std.traits : isSomeChar, isStaticArray, isArray; import std.algorithm : map; File f; this(File f) { this.f = f; } char[512] lineBuf; char[] line; private bool succW() { import std.range.primitives : empty, front, popFront; import std.ascii : isWhite; while (!line.empty && line.front.isWhite) { line.popFront; } return !line.empty; } private bool succ() { import std.range.primitives : empty, front, popFront; import std.ascii : isWhite; while (true) { while (!line.empty && line.front.isWhite) { line.popFront; } if (!line.empty) break; line = lineBuf[]; f.readln(line); if (!line.length) return false; } return true; } private bool readSingle(T)(ref T x) { import std.algorithm : findSplitBefore; import std.string : strip; import std.conv : parse; if (!succ()) return false; static if (isArray!T) { alias E = ElementType!T; static if (isSomeChar!E) { auto r = line.findSplitBefore(" "); x = r[0].strip.dup; line = r[1]; } else static if (isStaticArray!T) { foreach (i; 0..T.length) { bool f = succW(); assert(f); x[i] = line.parse!E; } } else { FastAppender!(E[]) buf; while (succW()) { buf ~= line.parse!E; } x = buf.data; } } else { x = line.parse!T; } return true; } int read(T, Args...)(ref T x, auto ref Args args) { if (!readSingle(x)) return 0; static if (args.length == 0) { return 1; } else { return 1 + read(args); } } } /* IMPORT /Users/yosupo/Program/dcomp/source/dcomp/foundation.d */ // module dcomp.foundation; static if (__VERSION__ <= 2070) { /* Copied by https://github.com/dlang/phobos/blob/master/std/algorithm/iteration.d Copyright: Andrei Alexandrescu 2008-. License: $(HTTP boost.org/LICENSE_1_0.txt, Boost License 1.0). */ template fold(fun...) if (fun.length >= 1) { auto fold(R, S...)(R r, S seed) { import std.algorithm : reduce; static if (S.length < 2) { return reduce!fun(seed, r); } else { import std.typecons : tuple; return reduce!fun(tuple(seed), r); } } } } version (X86) static if (__VERSION__ < 2071) { import core.bitop : bsf, bsr, popcnt; int bsf(ulong v) { foreach (i; 0..64) { if (v & (1UL << i)) return i; } return -1; } int bsr(ulong v) { foreach_reverse (i; 0..64) { if (v & (1UL << i)) return i; } return -1; } int popcnt(ulong v) { int c = 0; foreach (i; 0..64) { if (v & (1UL << i)) c++; } return c; } } /* IMPORT /Users/yosupo/Program/dcomp/source/dcomp/ldc/inline.d */ // module dcomp.ldc.inline; version(LDC) { pragma(LDC_inline_ir) R inlineIR(string s, R, P...)(P); } /* IMPORT /Users/yosupo/Program/dcomp/source/dcomp/int128.d */ // module dcomp.int128; // import dcomp.array; version(LDC) { // import dcomp.ldc.inline; } version(LDC) version(X86_64) { version = LDC_IR; } ulong[2] mul128(ulong a, ulong b) { ulong[2] res; version(LDC_IR) { ulong upper, lower; inlineIR!(` %r0 = zext i64 %0 to i128 %r1 = zext i64 %1 to i128 %r2 = mul i128 %r1, %r0 %r3 = trunc i128 %r2 to i64 %r4 = lshr i128 %r2, 64 %r5 = trunc i128 %r4 to i64 store i64 %r3, i64* %2 store i64 %r5, i64* %3`, void)(a, b, &lower, &upper); return [lower, upper]; } else version(D_InlineAsm_X86_64) { ulong upper, lower; asm { mov RAX, a; mul b; mov lower, RAX; mov upper, RDX; } return [lower, upper]; } else { ulong B = 2UL^^32; ulong[2] a2 = [a % B, a / B]; ulong[2] b2 = [b % B, b / B]; ulong[4] c; foreach (i; 0..2) { foreach (j; 0..2) { c[i+j] += a2[i] * b2[j] % B; c[i+j+1] += a2[i] * b2[j] / B; } } foreach (i; 0..3) { c[i+1] += c[i] / B; c[i] %= B; } return [c[0] + c[1] * B, c[2] + c[3] * B]; } } ulong div128(ulong[2] a, ulong b) { version(LDC_IR) { return inlineIR!(` %r0 = zext i64 %0 to i128 %r1 = zext i64 %1 to i128 %r2 = shl i128 %r1, 64 %r3 = add i128 %r0, %r2 %r4 = zext i64 %2 to i128 %r5 = udiv i128 %r3, %r4 %r6 = trunc i128 %r5 to i64 ret i64 %r6`,ulong)(a[0], a[1], b); } else version(D_InlineAsm_X86_64) { ulong upper = a[1], lower = a[0]; ulong res; asm { mov RDX, upper; mov RAX, lower; div b; mov res, RAX; } return res; } else { import std.bigint, std.conv; return (((BigInt(a[1]) << 64) + BigInt(a[0])) / BigInt(b)).to!string.to!ulong; } } /* This source code generated by dcomp and include dcomp's source code. dcomp's Copyright: Copyright (c) 2016- Kohei Morita. (https://github.com/yosupo06/dcomp) dcomp's License: MIT License(https://github.com/yosupo06/dcomp/blob/master/LICENSE.txt) */