int gcd(int a, int b) {if (b > a) {return gcd(b, a);} if (b == 0) {return a;} return gcd(b, a % b);}int expo(int a, int b, int mod) {int res = 1; while (b > 0) {if (b & 1)res = (res * a) % mod; a = (a * a) % mod; b = b >> 1;} return res;}void extendgcd(int a, int b, int*v) {if (b == 0) {v[0] = 1; v[1] = 0; v[2] = a; return ;} extendgcd(b, a % b, v); int x = v[1]; v[1] = v[0] - v[1] * (a / b); v[0] = x; return;} int mminv(int a, int b) {int arr[3]; extendgcd(a, b, arr); return arr[0];}int mminvprime(int a, int b) {return expo(a, b - 2, b);}bool revsort(int a, int b) {return a > b;}int combination(int n, int r, int m, int *fact, int *ifact) {int val1 = fact[n]; int val2 = ifact[n - r]; int val3 = ifact[r]; return (((val1 * val2) % m) * val3) % m;}void google(int t) {cout << "Case #" << t << ": ";}vector<int> sieve(int n) {int*arr = new int[n + 1](); vector<int> vect; for (int i = 2; i <= n; i++)if (arr[i] == 0) {vect.push_back(i); for (int j = 2 * i; j <= n; j += i)arr[j] = 1;} delete[] arr; return vect;}int mod_add(int a, int b, int m) {a = a % m; b = b % m; return (((a + b) % m) + m) % m;}int mod_mul(int a, int b, int m) {a = a % m; b = b % m; return (((a * b) % m) + m) % m;}int mod_sub(int a, int b, int m) {a = a % m; b = b % m; return (((a - b) % m) + m) % m;}int mod_div(int a, int b, int m) {a = a % m; b = b % m; return (mod_mul(a, mminvprime(b, m), m) + m) % m;}int phin(int n) {int number = n; if (n % 2 == 0) {number /= 2; while (n % 2 == 0) n /= 2;} for (int i = 3; i <= sqrt(n); i += 2) {if (n % i == 0) {while (n % i == 0)n /= i; number = (number / i * (i - 1));}} if (n > 1)number = (number / n * (n - 1)); return number;}