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- #include<bits/stdc++.h>
- using namespace std;
- // #pragma GCC optimize("Ofast,no-stack-protector")
- // #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
- // #pragma GCC optimize("unroll-loops")
- typedef unsigned long long ull;
- typedef long long ll;
- typedef long double lld;
- typedef vector<int> vi;
- typedef vector<ll> vll;
- typedef vector<vi> vvi;
- typedef pair<int,int > pii;
- typedef pair<ll,ll > pll;
- typedef vector< pii > vpii;
- typedef vector< pll > vpll;
- typedef set<int> sti;
- #define sc scanf
- #define pf printf
- #define sci(n) scanf("%d",&n)
- #define scii(n,m) scanf("%d %d",&n,&m)
- #define scl(n) scanf("%lld",&n)
- #define scd(n) scanf("%lf",&n)
- #define scs(s) scanf("%s",s)
- #define pfi(n) printf("%d",n)
- #define pfl(n) printf("%lld",n)
- #define pff(n) cout<<n
- #define spc printf(" ")
- #define line printf("\n")
- #define loop(i,x,y) for(int i=int(x); i<=int(y); i++)
- #define rloop(i,y,x) for(int i=int(y); i>=int(x); i--)
- #define cspf(i) printf("Case %d: ", i)
- #define vout(v) for(int w=0;w<v.size();w++){if(w) cout<<' '; cout<<v[w];}
- #define clr(a,x) memset(a,x,sizeof(a))
- #define tp(v,j) get<j>(v)
- #define pb push_back
- #define mp make_pair
- #define mt make_tuple
- #define ff first
- #define ss second
- #define all(v) v.begin(),v.end()
- #define rall(v) v.rbegin(),v.rend()
- #define read() freopen("input.txt", "r", stdin)
- #define write() freopen("output.txt", "w", stdout)
- #define fastIO() ios_base::sync_with_stdio(false); cin.tie(NULL);
- /// Constants
- #define eps 1e-6
- #define PI acos(-1.0) // 3.1415926535897932
- #define MAX (ll)2147483647
- #define MAXn 1000009
- int GCD(int a, int b) { return b == 0 ? a : GCD(b , a % b); }
- ll LCM(ll a, ll b) { return a * (b/GCD(a, b)); }
- bool isprime(ll n)
- {
- if(n%2==0) return false;
- for(ll i=3;i*i<=n;i+=2){
- if(n%i==0) return false;
- }
- return true;
- }
- ll BigMod(ll base,ll power,ll mod)
- {
- ll res = 1;
- base = base % mod;
- while(power > 0){
- if(power % 2) res = (res * base) % mod;
- power = power/2;
- base = (base * base) % mod;
- }
- return res;
- }
- bool is_Carmichael(ll n)
- {
- for(ll a = 2; a < n; a++){
- if(BigMod(a,n,n) != a) return false;
- }
- return true;
- }
- int main()
- {
- #ifdef VAMP
- clock_t tStart = clock();
- freopen("input.txt", "r", stdin);
- freopen("output.txt", "w", stdout);
- #endif
- while(1){
- ll n;
- scl(n);
- if(!n) break;
- if(!isprime(n) && is_Carmichael(n)) pf("The number %lld is a Carmichael number.\n",n);
- else pf("%lld is normal.\n",n);
- }
- #ifdef VAMP
- fprintf(stderr, "\n>> Runtime: %.10fs\n", (double) (clock() - tStart) / CLOCKS_PER_SEC);
- #endif
- return 0;
- }
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