#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>#define int64 __int64using namespace std;int64 MOD[]={13251349,13251361,13251367, 13251373,13251377,13251383}; int64 prime[60000],isprime[60000],cnt; void init() { int64 i,j; cnt=0; for(i=2;i<60000;i++) { if(!isprime[i]) prime[++cnt]=i; for(j=1;j<=cnt&′[j]*i<60000;j++) { isprime[prime[j]*i]=1; if(i%prime[j]==0) break; } } } struct node { int64 prime,num; }; node a[100]; int64 n,aNum,factor[10000],factorNum; int64 coef[105]; int64 ABS(int64 x) { if(x<0) return -x; return x; } void DFS(int64 x,int dep) { int64 i; if(dep==aNum+1) { factor[factorNum++]=x; } else { for(i=0;i<=a[dep].num;i++) { DFS(x,dep+1); x=x*a[dep].prime; } } } void cal(int64 p) { aNum=0; int64 i; for(i=1;i<=cnt;i++) if(p%prime[i]==0) { aNum++; a[aNum].prime=prime[i]; a[aNum].num=0; while(p%prime[i]==0) { a[aNum].num++; p/=prime[i]; } } if(p>1) { aNum++; a[aNum].prime=p; a[aNum].num=1; } factorNum=0; DFS(1,1); } int OK(int64 a) { int64 r,b,i,j; for(i=0;i<6;i++) { r=0; b=a%MOD[i]; for(j=n;j>=0;j--) r=(r*b+coef[j])%MOD[i]; if(r) return 0; } return 1; } int64 ans[10005],ansNum; int main() { init(); while(scanf("%d",&n)!=-1) { int64 i,j,k,t,r,u; for(i=n-1;i>=0;i--) scanf("%I64d",&coef[i]); coef[n]=1; ansNum=0; k=0; factorNum=0; while(n) { if(coef[0]==0) { ans[ansNum++]=0; for(i=0;i<n;i++) coef[i]=coef[i+1]; n--; } else { if(!factorNum) cal(ABS(coef[0])); t=0; for(i=k;i<factorNum;i++) if(coef[0]%factor[i]==0) { if(OK(factor[i])) { t=factor[i]; k=i; break; } if(OK(-factor[i])) { t=-factor[i]; k=i; break; } } if(!t) break; ans[ansNum++]=t; r=0; for(i=n;i>=0;i--) { u=r*t+coef[i]; coef[i]=r; r=u; } n--; } } sort(ans,ans+ansNum); printf("%I64dn",ansNum); for(i=0;i<ansNum;i++) printf("%I64dn",ans[i]); } return 0; }
