// URL: https://yukicoder.me/problems/no/312 import std.algorithm, std.array, std.bitmanip, std.container, std.conv, std.format, std.functional, std.math, std.range, std.traits, std.typecons, std.stdio, std.string; version(unittest) {} else void main() { long N; io.getV(N); auto pf = primeFactorSqrtOf(N), d = pf.divisors(N); io.put(d.filter!"a>2".front); } pure nothrow @nogc @safe { auto lowerBoundBy(alias conv = "a", alias comp = "a tuple(e, convFun(e))).assumeSorted!((a, b) => compFun(a[1], b[1])); } } pure nothrow @nogc @safe { T isqrt(T)(T n) if (is(T == int) || is(T == long)) { static if (is(T == int)) auto max = 46_341; else static if (is(T == long)) auto max = 3_037_000_500L; return iota(T(0), max).lowerBoundBy!("a^^2", "a<=b")(n).back; } T icbrt(T)(T n) if (is(T == int) || is(T == long)) { static if (is(T == int)) auto max = 1_291; else static if (is(T == long)) auto max = 2_097_152L; return iota(T(0), max).lowerBoundBy!("a^^3", "a<=b")(n).back; } } struct PrimeFactor { struct Factor(T) { T prime; int exp; } const int n; int[] primes; pure nothrow { this(int n) { this.n = n; auto sieve = BitArray(); sieve.length((n+1)/2); sieve = ~sieve; foreach (p; 1..(n.isqrt-1)/2+1) if (sieve[p]) for (auto q = p*3+1; q < (n+1)/2; q += p*2+1) sieve[q] = false; primes = sieve.bitsSet.map!(p => cast(int)p*2+1).array; primes[0] = 2; } } pure nothrow @safe { Factor!T[] div(T)(T x) const if (isIntegral!T) in { assert(x > 0 && x.isqrt <= n); } do { Factor!T[] factors; auto t = isqrt(x); foreach (p; primes) { if (p > t) break; auto c = 0; for (; x%p == 0; x /= p) ++c; if (c > 0) factors ~= Factor!T(p, c); if (x == 1) break; } if (x > 1) factors ~= [Factor!T(x, 1)]; return factors; } T[] divisors(T)(T x) const if (isIntegral!T) in { assert(x > 0 && x.isqrt <= n); } do { auto factors = div(x); auto r = divisorsProc(factors, 0, 1); r.sort(); return r; } } private { pure nothrow @safe { T[] divisorsProc(T)(const Factor!T[] factors, int i, T c) const { if (i == factors.length) return [c]; T[] r; foreach (j; 0..factors[i].exp+1) r ~= divisorsProc(factors, i+1, c*factors[i].prime^^j); return r; } } } } pure nothrow { auto primeFactor(int n) { return PrimeFactor(n); } auto primeFactorSqrtOf(T)(T n) if (isIntegral!T) { return PrimeFactor(cast(int)n.isqrt); } } auto io = IO!()(); import std.stdio; struct IO(alias IN = stdin, alias OUT = stdout) { import std.meta : allSatisfy; import core.stdc.stdlib : exit; void getV(T...)(ref T v) { foreach (ref w; v) get(w); } void getA(T)(size_t n, ref T v) if (hasAssignableElements!T) { v = new T(n); foreach (ref w; v) get(w); } void getC(T...)(size_t n, ref T v) if (allSatisfy!(hasAssignableElements, T)) { foreach (ref w; v) w = new typeof(w)(n); foreach (i; 0..n) foreach (ref w; v) get(w[i]); } void getM(T)(size_t r, size_t c, ref T v) if (hasAssignableElements!T && hasAssignableElements!(ElementType!T)) { v = new T(r); foreach (ref w; v) getA(c, w); } template getS(E...) { void getS(T)(size_t n, ref T v) { v = new T(n); foreach (ref w; v) foreach (e; E) mixin("get(w."~e~");"); } } const struct PutConf { bool newline = true, flush, exit; string floatFormat = "%.10f", delimiter = " "; } void put(alias conf = "{}", T...)(T v) { mixin("const PutConf c = "~conf~"; putMain!c(v);"); } void putB(alias conf = "{}", S, T)(bool c, S t, T f) { if (c) put!conf(t); else put!conf(f); } void putRaw(T...)(T v) { OUT.write(v); OUT.writeln; } private { dchar[] buf; auto sp = (new dchar[](0)).splitter; void nextLine() { IN.readln(buf); sp = buf.splitter; } void get(T)(ref T v) { if (sp.empty) nextLine(); v = sp.front.to!T; sp.popFront(); } void putMain(PutConf c, T...)(T v) { foreach (i, w; v) { putOne!c(w); if (i+1 < v.length) OUT.write(c.delimiter); } static if (c.newline) OUT.writeln; static if (c.flush) OUT.flush(); static if (c.exit) exit(0); } void putOne(PutConf c, T)(T v) { static if (isInputRange!T && !isSomeString!T) putRange!c(v); else static if (isFloatingPoint!T) OUT.write(format(c.floatFormat, v)); else static if (hasMember!(T, "fprint")) v.fprint(OUT); else OUT.write(v); } void putRange(PutConf c, T)(T v) { auto w = v; while (!w.empty) { putOne!c(w.front); w.popFront(); if (!w.empty) OUT.write(c.delimiter); } } } }