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struct fastIO{
char s[100000]; int it,len;
fastIO(){it = len = 0;}
inline char get(){
if (it < len) return s[it++];
it = 0; len = fread(s, 1, 100000, stdin);
if (len == 0) return EOF;
else return s[it++];
}
bool notend(){
char c = get();
while(c == ' ' || c == '\n') c = get();
if (it > 0) it--;
return c != EOF;
}
}_buff;
inline ll getNum(){
ll r = 0; bool ng = 0;
char c = _buff.get();
while (c != '-' && (c < '0' || c > '9')) c = _buff.get();
if (c == '-') ng = 1, c = _buff.get();
while (c >= '0' && c <= '9') r = r * 10 + c - '0', c = _buff.get();
return ng ? -r : r;
}