Crazy Professor

http://acm.timus.ru/problem.aspx?space=1&num=1682

记录取模的余数，并查集。

const int MM = 511111;
#define debug puts("wrong")
typedef __int64 int64;
int64 N;
bool vis[MM];
vector<int64>g[MM];
vector<int64>gg[MM]; //^2

int64 fa[MM], ran[MM];
int64 getfa(int64 x) {return x==fa[x]?x:fa[x]=getfa(fa[x]);}
void get_init() {
    for(int64 i=0;i<MM;i++) fa[i]=i, ran[i]=0;
}
void join(int64 x,int64 y) {
    if(ran[x]>ran[y]) fa[y]=x;
    else {
        fa[x]=y;
        if(ran[y]==ran[x]) ran[y]++; 
    }
}

void solve() {
    int64 i,j,k,tmp,tt,xx,yy,v;
    bool ff;
    for(i=0;i<MM;i++) g[i].clear(),gg[i].clear();
    get_init();
    if(N==1) {printf("3\n");return;} 
    for(i=1;i<MM;i++) {
        tmp=(i*i)%N, tt=i%N;
        for(j=0;j<g[N-tmp].size();j++) {
            v=g[N-tmp][j];
            xx=getfa(i), yy=getfa(v);
            if(xx==yy) {printf("%I64d\n",i);return;}
            else join(xx,yy);
        }
        for(j=0;j<gg[N-tt].size();j++) {
            v=gg[N-tt][j];
            if((i*i+v)%N==0) continue;
            xx=getfa(i), yy=getfa(v);
            if(xx==yy) {printf("%I64d\n",i);return;}
            else join(xx,yy);
        }
        gg[tmp].push_back(i); g[tt].push_back(i);
    }
    printf("-1\n");
}
int main() {
//    freopen("out.txt","w",stdout);
    while(scanf("%I64d",&N)!=EOF) solve();
    return 0;
}