LA 3523

#include<stdio.h>
#include<string.h>
const int N = 1010;
const int M = 3000000;
struct Edge {
int u, v, next;
Edge() {}
Edge(int u, int v, int next) : u(u), v(v), next(next) {}
}E[M];
int head
, tot;

void addEdge(int u, int v) {
E[tot] = Edge(u, v, head[u]);
head[u] = tot++;
E[tot] = Edge(v, u, head[v]);
head[v] = tot++;
}

int pre
, iscut
, bccno
, dfs_colock, bcc_cnt, bcc

, bcc_size
;
Edge S[M];
int ST;

int color
;
bool bipartite(int u, int b) {
for(int i = head[u]; i != -1; i = E[i].next) {
int v = E[i].v; if(bccno[v] != b) continue;
if(color[v] == color[u]) return false;
if(!color[v]) {
color[v] = 3 - color[u];
if(!bipartite(v, b)) return false;
}
}
return true;
}

int min(int a, int b) { return a < b ?  a : b; }
int dfs(int u, int fa) {
int lowu = pre[u] = ++dfs_colock;
int child = 0;
for(int i = head[u]; i != -1; i = E[i].next) {
int v = E[i].v;
Edge e = Edge(u, v, -1);
if(!pre[v]) {
S[++ST] = e;
child++;
int lowv = dfs(v, u);
lowu = min(lowu, lowv);
if(lowv >= pre[u]) {
iscut[u] = true;
bcc_cnt++; bcc_size[bcc_cnt] = 0;
while(1) {
Edge x = S[ST--];
if(bccno[x.u] != bcc_cnt) {
bcc[bcc_cnt][bcc_size[bcc_cnt]++] = x.u;
bccno[x.u] = bcc_cnt;
}
if(bccno[x.v] != bcc_cnt) {
bcc[bcc_cnt][bcc_size[bcc_cnt]++] = x.v;
bccno[x.v] = bcc_cnt;
}
if(x.u == u && x.v == v) break;
}
}
}
else if(pre[v] < pre[u] && v != fa) {
S[++ST] = e;
lowu = min(lowu, pre[v]);
}
}
if(fa < 0 && child == 1) iscut[u] = 0;
return lowu;
}

void find_bcc(int n) {
memset(pre, 0, sizeof(pre));
memset(iscut, 0, sizeof(iscut));
memset(bccno, 0, sizeof(bccno));
dfs_colock = bcc_cnt = 0;
for(int i = 0; i < n; ++i)
if(!pre[i]) dfs(i, -1);
}
int A

;
int main() {
int kase = 0, n, m;
while(scanf("%d%d", &n, &m) && n) {
memset(head, -1, sizeof(head));
memset(A, 0, sizeof(A));
for(int i = 0; i < m; ++i) {
int u, v;
scanf("%d%d", &u, &v); u--; v--; A[u][v] = A[v][u] = 1;
}
for(int i = 0; i < n; ++i)
for(int j = i + 1; j < n; ++j)
if(!A[i][j]) addEdge(i, j);
find_bcc(n);
int odd
={0};
for(int i = 1; i<= bcc_cnt; ++i) {
memset(color, 0, sizeof(color));
for(int j = 0; j < bcc_size[i]; ++j) bccno[bcc[i][j]] = i;
int u = bcc[i][0];
color[u] = 1;
if(!bipartite(u, i))
for(int j = 0; j < bcc_size[i]; ++j) odd[bcc[i][j]] = 1;
}
int ans = n;
for(int i = 0; i < n; ++i) if(odd[i]) ans--;
printf("%d\n", ans);
}
return 0;
}