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#include "../template.hh"
template<int N>
struct SVL : array<int, N + 1> {
vi ps;
SVL() : array<int, N + 1>{} {
FOR (i, 2, N + 1) {
if ((*this)[i] == 0) ps.pb((*this)[i] = i);
for (int j = 0; j < SZ(ps) && ps[j] <= (*this)[i] && i * ps[j] <= N; ++j) {
(*this)[i * ps[j]] = ps[j];
}
}
}
bool is_prime(int n) { return n == (*this)[n]; };
};
SVL<(int)1e7> sv;
#line 1 "code/template.cc"
// this line is here for a reason
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> ii;
typedef vector<int> vi;
typedef vector<ii> vii;
typedef vector<vi> vvi;
typedef vector<vii> vvii;
#define fi first
#define se second
#define eb emplace_back
#define pb push_back
#define mp make_pair
#define mt make_tuple
#define endl '\n'
#define ALL(x) (x).begin(), (x).end()
#define RALL(x) (x).rbegin(), (x).rend()
#define SZ(x) (int)(x).size()
#define FOR(a, b, c) for (auto a = (b); (a) < (c); ++(a))
#define F0R(a, b) FOR (a, 0, (b))
template <typename T>
bool ckmin(T& a, const T& b) { return a > b ? a = b, true : false; }
template <typename T>
bool ckmax(T& a, const T& b) { return a < b ? a = b, true : false; }
#ifndef DEBUG
#define DEBUG 0
#endif
#define dout if (DEBUG) cerr
#define dvar(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] "
#line 2 "code/math/SVL.cc"
template<int N>
struct SVL : array<int, N + 1> {
vi ps;
SVL() : array<int, N + 1>{} {
FOR (i, 2, N + 1) {
if ((*this)[i] == 0) ps.pb((*this)[i] = i);
for (int j = 0; j < SZ(ps) && ps[j] <= (*this)[i] && i * ps[j] <= N; ++j) {
(*this)[i * ps[j]] = ps[j];
}
}
}
bool is_prime(int n) { return n == (*this)[n]; };
};
SVL<(int)1e7> sv;