MOD = 998244353i64 mat = Matrix(Int64).new(8, 8) mat[0][0] = 1 mat[1][0] = 1 mat[2][0] = 1 mat[3][0] = 1 mat[0][1] = 1 mat[1][1] = 1 mat[2][1] = 1 mat[3][1] = 1 mat[2][2] = 1 mat[3][2] = 1 mat[4][2] = 1 mat[5][2] = 1 mat[2][3] = 1 mat[3][3] = 1 mat[4][3] = 1 mat[5][3] = 1 mat[4][4] = 1 mat[5][4] = 1 mat[6][4] = 1 mat[7][4] = 1 mat[4][5] = 1 mat[5][5] = 1 mat[6][5] = 1 mat[7][5] = 1 mat[6][6] = 1 mat[1][6] = 1 mat[2][6] = 1 mat[3][6] = 1 mat[6][7] = 1 mat[7][7] = 1 mat2 = Matrix(Int64).new(2, 2) mat2[0][0] = 1 mat2[1][0] = 1 mat2[0][1] = 1 mat2[1][1] = 1 read_line.to_i.times do n = read_line.to_i64 m = mat.pow(n) m2 = mat2.pow(n) puts (m[0][0] + m[6][0] - m2[0][0] + MOD) % MOD end class Matrix(T) @a : Array(Array(T)) getter :a, :d1, :d2 def initialize(n : Int32, m : Int32) @a = Array.new(n) { Array.new(m, T.zero) } @d1 = n @d2 = m end def clone ret = Matrix(T).new(@d1, @d2) @d1.times do |i| @d2.times do |j| ret.a[i][j] = @a[i][j] end end return ret end def [](idx : Int32) return @a[idx] end def mul(other : Matrix(T)) if @d2 != other.d1 raise ArgumentError.new end d3 = other.d2 tmp = Array.new(d3) { Array.new(@d2, T.zero) } d3.times do |i| tr1 = tmp[i] @d2.times do |j| tr1[j] = other[j][i] end end ret = Array.new(@d1) { Array.new(d3, T.zero) } @d1.times do |i| row1 = @a[i] ret1 = ret[i] d3.times do |j| sum = T.zero row2 = tmp[j] @d2.times do |k| sum += row1[k] * row2[k] sum %= MOD end ret1[j] = sum end end @a = ret end def mul_l(other : Matrix(T)) # in-place if other.d2 != @d1 raise ArgumentError.new end d3 = @d2 tmp = Array.new(d3) { Array.new(@d1, T.zero) } d3.times do |i| tr1 = tmp[i] @d1.times do |j| tr1[j] = @a[j][i] end end other.d1.times do |i| row1 = other.a[i] ret1 = @a[i] d3.times do |j| sum = T.zero row2 = tmp[j] other.d2.times do |k| sum += row1[k] * row2[k] sum %= MOD end ret1[j] = sum end end end def pow(p : Int64) b = Matrix(T).new(@d1, @d2) ret = Matrix(T).new(@d1, @d2) @d1.times do |i| @d2.times do |j| b.a[i][j] = @a[i][j] % MOD end ret.a[i][i] = 1 end while p > 0 if (p & 1) != 0 ret.mul_l(b) end b.mul(b) p >>= 1 end return ret end end