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#include "others/fastIO.hpp"
namespace FastIO {
struct PreCalc {
char num[10000 * 4];
constexpr PreCalc() : num(){
for(int i = 0; i < 10000; i++){
int t = i;
for(int j = 3; j >= 0; j--){
num[i*4 + j] = (t % 10) + '0';
t /= 10;
}
}
}
};
static constexpr PreCalc pr;
struct FastIO {
template <class T>
using enable_if_integer = enable_if_t<is_integral<T>::value || is_same<T, __int128_t>::value || is_same<T, __uint128_t>::value>;
static constexpr int buf_size = 1 << 20;
static constexpr int rem = 1 << 6;
char in_buf[buf_size], *in_cur = in_buf + buf_size;
char out_buf[buf_size], *out_cur = out_buf;
FastIO(){ load(); }
~FastIO(){ flush(); }
void load(){
const int len = in_buf + buf_size - in_cur;
memmove(in_buf, in_cur, len);
in_cur = in_buf;
fread(in_buf + len, 1, buf_size - len, stdin);
}
void flush(){
fwrite(out_buf, 1, out_cur - out_buf, stdout);
out_cur = out_buf;
}
void through(){
if(in_cur - in_buf >= buf_size - rem) load();
while(*in_cur <= ' ') in_cur++;
assert(in_buf <= in_cur && in_cur < in_buf + buf_size);
}
#define gc() (*in_cur++)
template <class T, enable_if_integer<T>* = nullptr>
inline void read(T &x){
through();
bool neg = false;
int c = gc();
if(c == '-') neg = true, c = gc();
x = c^'0'; c = gc();
while(c >= '0' && c <= '9') x = x*10 + (c^'0'), c = gc();
if(neg) x = -x;
}
inline void read(string &x){
through();
x.clear();
while(true){
char *p = in_cur;
while(*p > ' ' && p - in_buf < buf_size - rem) p++;
copy(in_cur, p, back_inserter(x));
in_cur = p;
if(*p <= ' ') break;
load();
}
}
inline void read(char &x){
through();
x = gc();
}
#undef gc
#define pc(c) *out_cur++ = (c)
template <class T, enable_if_integer<T>* = nullptr>
inline void out(T x){
static constexpr int tmp_size = sizeof(T)*5/2;
static char tmp[tmp_size];
if(out_cur - out_buf >= buf_size - rem) flush();
if(!x){ pc('0'); return; }
if(x < 0){ pc('-'); x = -x; }
int idx = tmp_size;
while(x >= 10000){
idx -= 4;
memcpy(tmp + idx, pr.num + (x % 10000)*4, 4);
x /= 10000;
}
if(x < 100){
if(x < 10){
pc(x + '0');
}else{
pc(x/10 + '0');
pc(x%10 + '0');
}
}else{
if(x < 1000){
memcpy(out_cur, pr.num + x*4 + 1, 3);
out_cur += 3;
}else{
memcpy(out_cur, pr.num + x*4, 4);
out_cur += 4;
}
}
memcpy(out_cur, tmp + idx, tmp_size - idx);
out_cur += tmp_size - idx;
}
inline void out(const string &s){
flush();
fwrite(s.c_str(), 1, s.size(), stdout);
}
inline void out(const char c){
if(out_cur - out_buf >= buf_size - rem) flush();
pc(c);
}
#undef pc
template <class T>
friend FastIO &operator>>(FastIO &io, T &x){
io.read(x);
return io;
}
template <class T>
friend FastIO &operator<<(FastIO &io, const T &x){
io.out(x);
return io;
}
};
FastIO io;
} // namespace FastIO
using FastIO::io;
#define cin io
#define cout io
#line 1 "others/fastIO.hpp"
namespace FastIO {
struct PreCalc {
char num[10000 * 4];
constexpr PreCalc() : num(){
for(int i = 0; i < 10000; i++){
int t = i;
for(int j = 3; j >= 0; j--){
num[i*4 + j] = (t % 10) + '0';
t /= 10;
}
}
}
};
static constexpr PreCalc pr;
struct FastIO {
template <class T>
using enable_if_integer = enable_if_t<is_integral<T>::value || is_same<T, __int128_t>::value || is_same<T, __uint128_t>::value>;
static constexpr int buf_size = 1 << 20;
static constexpr int rem = 1 << 6;
char in_buf[buf_size], *in_cur = in_buf + buf_size;
char out_buf[buf_size], *out_cur = out_buf;
FastIO(){ load(); }
~FastIO(){ flush(); }
void load(){
const int len = in_buf + buf_size - in_cur;
memmove(in_buf, in_cur, len);
in_cur = in_buf;
fread(in_buf + len, 1, buf_size - len, stdin);
}
void flush(){
fwrite(out_buf, 1, out_cur - out_buf, stdout);
out_cur = out_buf;
}
void through(){
if(in_cur - in_buf >= buf_size - rem) load();
while(*in_cur <= ' ') in_cur++;
assert(in_buf <= in_cur && in_cur < in_buf + buf_size);
}
#define gc() (*in_cur++)
template <class T, enable_if_integer<T>* = nullptr>
inline void read(T &x){
through();
bool neg = false;
int c = gc();
if(c == '-') neg = true, c = gc();
x = c^'0'; c = gc();
while(c >= '0' && c <= '9') x = x*10 + (c^'0'), c = gc();
if(neg) x = -x;
}
inline void read(string &x){
through();
x.clear();
while(true){
char *p = in_cur;
while(*p > ' ' && p - in_buf < buf_size - rem) p++;
copy(in_cur, p, back_inserter(x));
in_cur = p;
if(*p <= ' ') break;
load();
}
}
inline void read(char &x){
through();
x = gc();
}
#undef gc
#define pc(c) *out_cur++ = (c)
template <class T, enable_if_integer<T>* = nullptr>
inline void out(T x){
static constexpr int tmp_size = sizeof(T)*5/2;
static char tmp[tmp_size];
if(out_cur - out_buf >= buf_size - rem) flush();
if(!x){ pc('0'); return; }
if(x < 0){ pc('-'); x = -x; }
int idx = tmp_size;
while(x >= 10000){
idx -= 4;
memcpy(tmp + idx, pr.num + (x % 10000)*4, 4);
x /= 10000;
}
if(x < 100){
if(x < 10){
pc(x + '0');
}else{
pc(x/10 + '0');
pc(x%10 + '0');
}
}else{
if(x < 1000){
memcpy(out_cur, pr.num + x*4 + 1, 3);
out_cur += 3;
}else{
memcpy(out_cur, pr.num + x*4, 4);
out_cur += 4;
}
}
memcpy(out_cur, tmp + idx, tmp_size - idx);
out_cur += tmp_size - idx;
}
inline void out(const string &s){
flush();
fwrite(s.c_str(), 1, s.size(), stdout);
}
inline void out(const char c){
if(out_cur - out_buf >= buf_size - rem) flush();
pc(c);
}
#undef pc
template <class T>
friend FastIO &operator>>(FastIO &io, T &x){
io.read(x);
return io;
}
template <class T>
friend FastIO &operator<<(FastIO &io, const T &x){
io.out(x);
return io;
}
};
FastIO io;
} // namespace FastIO
using FastIO::io;
#define cin io
#define cout io