struct fastio{
    char s[100005];
    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;
#define read(x) x=getnum()
#define write(x) putnum(x),putchar('\n')

inline LL getnum(){
    LL r=0;bool ng=0;char c;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;
}
template<class T> inline void putnum(T x){
    if(x<0)putchar('-'),x=-x;
    register short a[20]={},sz=0;
    while(x)a[sz++]=x%10,x/=10;
    if(sz==0)putchar('0');
    for(int i=sz-1;i>=0;i--)putchar('0'+a[i]);
}
inline char getreal(){char c=_buff.get();while(c<=32)c=_buff.get();return c;}