class Matrix(object): def __init__(self, nrow=1, ncol=1): self.nrow = nrow self.ncol = ncol self._data = [[0] * nrow for c in range(ncol)] def from2Dlist(self, data, shallow_copy=False): self.nrow = len(data) self.ncol = len(data[0]) for row in data: if len(row) != self.ncol: raise IndexError('All column lengths must be same.') if shallow_copy: self._data = data else: self._data = [row[:] for row in data] return self def makeIdentityMatrix(self, n): self.nrow = n self.ncol = n self._data = [[0] * n for c in range(n)] for i in range(n): self._data[i][i] = 1 return self def __getitem__(self, key): if isinstance(key, int): return self._data[key] row, col = key return self._data[row][col] def __setitem__(self, key, value): if isinstance(key, int): if len(value) == self.ncol: self._data[key] = value[:] else: raise IndexError('The length of value must be equal to ncol.') else: row, col = key self._data[row][col] = value def __mod__(self, modulo): mat = [[c % modulo for c in row] for row in self._data] return Matrix().from2Dlist(mat, shallow_copy=True) def __imod__(self, modulo): for row in self._data: for i in range(self.ncol): row[i] %= modulo return self def __add__(self, other): if self.nrow != other.nrow or self.ncol != other.ncol: raise TypeError('lhs and rhs must be same size.') mat = [] for row1, row2 in zip(self._data, other._data): row = [a + b for a, b in zip(row1, row2)] mat.append(row) return Matrix().from2Dlist(mat, shallow_copy=True) def __sub__(self, other): if self.nrow != other.nrow or self.ncol != other.ncol: raise TypeError('lhs and rhs must be same size.') mat = [] for row1, row2 in zip(self._data, other._data): row = [a - b for a, b in zip(row1, row2)] mat.append(row) return Matrix().from2Dlist(mat, shallow_copy=True) def __matmul__(self, other): if self.ncol != other.nrow: raise TypeError('ncol of lhs and nrow of rhs must be same.') mat = [] mat2 = other._data n = other.ncol for row1 in self._data: row = [sum(a * b[i] for a, b in zip(row1, mat2)) for i in range(n)] mat.append(row) return Matrix().from2Dlist(mat, shallow_copy=True) def __pow__(self, n, modulo = 0): if self.ncol != self.nrow: raise TypeError('operator pow (**) is not supproted when ncol != nrow.') mat = Matrix().from2Dlist(self._data) if modulo: mat %= modulo mat2 = Matrix().makeIdentityMatrix(self.ncol) while n: if n & 1: mat2 @= mat if modulo: mat2 %= modulo mat @= mat if modulo: mat %= modulo n >>= 1 return mat2 def pow(self, n, modulo = 0): if self.ncol != self.nrow: raise TypeError('operator pow (**) is not supproted when ncol != nrow.') mat = Matrix().from2Dlist(self._data) if modulo: mat %= modulo mat2 = Matrix().makeIdentityMatrix(self.ncol) while n: if n & 1: mat2 @= mat if modulo: mat2 %= modulo mat @= mat if modulo: mat %= modulo n >>= 1 return mat2 def __imatmul__(self, other): self = self.__matmul__(other) return self def __str__(self): return '\n'.join(map(str, self._data)) N = int(input()) def solve(N): mod = 10**9 + 7 a = solve_core(N, mod) if N % 11: b = '10' * ((N % 11) - 1) + '1' else: b = 0 return a, b def solve_core(N, mod): '''a[1] = 1, a[n+1] = 100*a[n] + 1 のとき、a[N] % mod を求める。 A = [[100, 1], [ 0, 1]] とすると、a[n] = A**n @ [[0], [1]] ''' A = Matrix().from2Dlist([[100, 1], [0, 1]]) An = pow(A, N, mod) return An[0][1] a, b = solve(N) print(a) print(b)