# require "/template" # require "./scanner" # ### Specifications # # ```plain # Inside input macro | Expanded code # ----------------------------------------------+--------------------------------------- # Uppercase string: Int32, Int64, Float64, etc. | {}.new(Scanner.s) # s | Scanner.s # c | Scanner.c # Other lowercase string: i, i64, f, etc. | Scanner.s.to_{} # operator[]: type[size] | Array.new(input(size)) { input(type) } # Tuple literal: {t1, t2, t3} | {input(t1), input(t2), input(t3)} # Array literal: [t1, t2, t3] | [input(t1), input(t2), input(t3)] # Range literal: t1..t2 | input(t1)..input(t2) # If: cond ? t1 : t2 | cond ? input(t1) : input(t2) # Assign: target = value | target = input(value) # ``` # # ### Examples # # Input: # ```plain # 5 3 # foo bar # 1 2 3 4 5 # ``` # ``` # n, m = input(Int32, Int64) # => {5, 10i64} # input(String, Char[m]) # => {"foo", ['b', 'a', 'r']} # input(Int32[n]) # => [1, 2, 3, 4, 5] # ``` # ``` # n, m = input(i, i64) # => {5, 10i64} # input(s, c[m]) # => {"foo", ['b', 'a', 'r']} # input(i[n]) # => [1, 2, 3, 4, 5] # ``` # # Input: # ```plain # 2 3 # 1 2 3 # 4 5 6 # ``` # # ``` # h, w = input(i, i) # => {2, 3} # input(i[h, w]) # => [[1, 2, 3], [4, 5, 6]] # ``` # ``` # input(i[i][i]) # => [[1, 2, 3], [4, 5, 6]] # ``` # # Input: # ```plain # 5 3 # 3 1 4 2 5 # 1 2 # 2 3 # 3 1 # ``` # ``` # n, m = input(i, i) # => {5, 3} # input(i.pred[n]) # => [2, 0, 3, 1, 4] # input({i - 1, i - 1}[m]) # => [{0, 1}, {1, 2}, {2, 0}] # ``` # # Input: # ```plain # 3 # 1 2 # 2 2 # 3 2 # ``` # ``` # input({tmp = i, tmp == 1 ? i : i.pred}[i]) # => [{1, 2}, {2, 1}, {3, 1}] # ``` # # Input: # ```plain # 3 # 1 2 # 2 3 # 3 1 # ``` # ``` # n = input(i) # input_column({Int32, Int32}, n) # => {[1, 2, 3], [2, 3, 1]} # ``` class Scanner private def self.skip_to_not_space peek = STDIN.peek not_space = peek.index { |x| x != 32 && x != 10 } || peek.size STDIN.skip(not_space) end def self.c skip_to_not_space STDIN.read_char.not_nil! end def self.s skip_to_not_space peek = STDIN.peek if index = peek.index { |x| x == 32 || x == 10 } STDIN.skip(index + 1) return String.new(peek[0, index]) end String.build do |buffer| loop do buffer.write peek STDIN.skip(peek.size) peek = STDIN.peek break if peek.empty? if index = peek.index { |x| x == 32 || x == 10 } buffer.write peek[0, index] STDIN.skip(index) break end end end end end macro internal_input(type, else_ast) {% if Scanner.class.has_method?(type.id) %} Scanner.{{type.id}} {% elsif type.stringify == "String" %} Scanner.s {% elsif type.stringify == "Char" %} Scanner.c {% elsif type.stringify =~ /[A-Z][a-z0-9_]*/ %} {{type.id}}.new(Scanner.s) {% elsif String.has_method?("to_#{type}".id) %} Scanner.s.to_{{type.id}} {% else %} {{else_ast}} {% end %} end macro internal_input_array(type, args) {% for i in 0...args.size %} %size{i} = input({{args[i]}}) {% end %} {% begin %} {% for i in 0...args.size %} Array.new(%size{i}) { {% end %} input({{type.id}}) {% for i in 0...args.size %} } {% end %} {% end %} end macro input(type) {% if type.is_a?(Call) %} {% if type.receiver.is_a?(Nop) %} internal_input( {{type.name}}, {{type.name}}( {% for argument in type.args %} input({{argument}}), {% end %} ) ) {% elsif type.name.stringify == "[]" %} internal_input_array({{type.receiver}}, {{type.args}}) {% else %} input({{type.receiver}}).{{type.name.id}}( {% for argument in type.args %} input({{argument}}), {% end %} ) {{type.block}} {% end %} {% elsif type.is_a?(TupleLiteral) %} { {% for i in 0...type.size %} input({{type[i]}}), {% end %} } {% elsif type.is_a?(ArrayLiteral) %} [ {% for i in 0...type.size %} input({{type[i]}}), {% end %} ] {% elsif type.is_a?(RangeLiteral) %} Range.new(input({{type.begin}}), input({{type.end}}), {{type.excludes_end?}}) {% elsif type.is_a?(If) %} {{type.cond}} ? input({{type.then}}) : input({{type.else}}) {% elsif type.is_a?(Assign) %} {{type.target}} = input({{type.value}}) {% else %} internal_input({{type.id}}, {{type.id}}) {% end %} end macro input(*types) { {% for type in types %} input({{type}}), {% end %} } end macro input_column(types, size) {% for type, i in types %} %array{i} = Array({{type}}).new({{size}}) {% end %} {{size}}.times do {% for type, i in types %} %array{i} << input({{type}}) {% end %} end { {% for type, i in types %} %array{i}, {% end %} } end # require "./tuple/times" struct Tuple def times(&block) : Nil {% begin %} {% for i in 0...@type.size %} {% if @type[i].has_method?(:each) %} self[{{i}}].each do |i{{i}}| {% else %} self[{{i}}].times do |i{{i}}| {% end %} {% end %} yield({% for i in 0...@type.size %} i{{i}}, {% end %}) {% for i in 0...@type.size %} end {% end %} {% end %} end private class TimesIterator(T) include Iterator(T) def initialize(@n : T) tuple = {% begin %} { {% for i in 0...T.size %} T[{{i}}].zero, {% end %} } {% end %} @index = tuple.as(T) @first = true end def next if @first @first = false return @index end {% begin %} {% type = @type.type_vars[0] size = type.size %} {% for i in 1..size %} if @index[{{size - i}}] < @n[{{size - i}}] - 1 @index = { {% for j in 0...size %} {% if j < size - i %} @index[{{j}}], {% elsif j == size - i %} @index[{{j}}] + 1, {% else %} {{type[j]}}.zero, {% end %} {% end %} } return @index end {% end %} stop {% end %} end end def times TimesIterator(self).new(self) end end # require "./comparable/min_max" module Comparable(T) def min(x : T) self > x ? x : self end def max(x : T) self < x ? x : self end end # require "./array/new" class Array def self.new(sizes : Tuple(*T), initial_value) forall T {% begin %} {% for i in 0...T.size %} Array.new(sizes[{{i}}]) { {% end %} initial_value {% for i in 0...T.size %} } {% end %} {% end %} end def self.new(sizes : Tuple(*T), &block) forall T {% begin %} {% for i in 0...T.size %} Array.new(sizes[{{i}}]) { |%i{i}| {% end %} yield({% for i in 0...T.size %} %i{i}, {% end %}) {% for i in 0...T.size %} } {% end %} {% end %} end end # require "./array/change" class Array(T) def chmin(i : Int, value : T) (self[i] > value).tap do |f| self[i] = value if f end end protected def chmin(i : Int, *indexes, value) self[i].chmin(*indexes, value: value) end def chmin(indexes : Tuple, value) chmin(*indexes, value: value) end def chmax(i : Int, value : T) (self[i] < value).tap do |f| self[i] = value if f end end protected def chmax(i : Int, *indexes, value) self[i].chmax(*indexes, value: value) end def chmax(indexes : Tuple, value) chmax(*indexes, value: value) end end # require "/math/mint" macro static_modint(name, mod) struct {{name}} MOD = {{mod}}i64 def self.zero new end def self.raw(value : Int64) result = new result.value = value result end macro [](*nums) {% verbatim do %} Array({{@type}}).build({{nums.size}}) do |%buffer| {% for num, i in nums %} %buffer[{{i}}] = {{@type}}.new({{num}}) {% end %} {{nums.size}} end {% end %} end getter value : Int64 def initialize @value = 0i64 end def initialize(value) @value = value.to_i64 % MOD end def initialize(m : self) @value = m.value end protected def value=(value : Int64) @value = value end def ==(m : self) value == m.value end def ==(m) value == m end def + : self self end def - : self self.class.raw(value != 0 ? MOD &- value : 0i64) end def +(v) self + self.class.new(v) end def +(m : self) x = value &+ m.value x &-= MOD if x >= MOD self.class.raw(x) end def -(v) self - self.class.new(v) end def -(m : self) x = value &- m.value x &+= MOD if x < 0 self.class.raw(x) end def *(v) self * self.class.new(v) end def *(m : self) self.class.new(value &* m.value) end def /(v) self / self.class.new(v) end def /(m : self) raise DivisionByZeroError.new if m.value == 0 a, b, u, v = m.value, MOD, 1i64, 0i64 while b != 0 t = a // b a &-= t &* b a, b = b, a u &-= t &* v u, v = v, u end self.class.new(value &* u) end def //(v) self / v end def **(exponent : Int) t, res = self, self.class.raw(1i64) while exponent > 0 res *= t if exponent & 1 == 1 t *= t exponent >>= 1 end res end {% for op in %w[< <= > >=] %} def {{op.id}}(other) raise NotImplementedError.new({{op}}) end {% end %} def inv self.class.raw(1) // self end def succ self.class.raw(value != MOD &- 1 ? value &+ 1 : 0i64) end def pred self.class.raw(value != 0 ? value &- 1 : MOD &- 1) end def abs self end def abs2 self * self end def to_i64 : Int64 value end delegate to_s, to: @value delegate inspect, to: @value end {% to = ("to_" + name.stringify.downcase.gsub(/mint|modint/, "m")).id %} struct Int {% for op in %w[+ - * / //] %} def {{op.id}}(value : {{name}}) {{to}} {{op.id}} value end {% end %} {% for op in %w[< <= > >=] %} def {{op.id}}(m : {{name}}) raise NotImplementedError.new({{op}}) end {% end %} def {{to}} : {{name}} {{name}}.new(self) end end class String def {{to}} : {{name}} {{name}}.new(self) end end end static_modint(Mint, 1000000007) static_modint(Mint2, 998244353) # require "/math/powmod" struct Int # Caluclates `self * exp % mod`. def powmod(exp : T, mod : self) forall T n = self % mod res = typeof(self).new(1) while exp > 0 res = res * n % mod if exp.odd? n = n * n % mod exp >>= 1 end res end end def min(c) sum = c.sum c.each_with_index.sum { |(cnt, x)| sum -= cnt (10.to_m ** cnt - 1) / 9 * x * 10.to_m**sum } end def min_mod(c, mod) index = Array(Int32?).new(mod, nil) cnt_to_mod = [] of Int32 cnt, now = 0, 1 cycle_size, cycle_start = 0, 0 loop do index[now] = cnt cnt_to_mod << now now = (now * 10 + 1) % mod cnt += 1 if prev = index[now] cycle_size, cycle_start = cnt - prev, now break end end line_size = index[cycle_start].not_nil! sum = c.sum c.each_with_index.sum { |(cnt, x)| sum -= cnt value = if cnt < line_size cnt_to_mod[cnt] else cnt_to_mod[line_size + (cnt - line_size) % cycle_size] end value * x % mod * 10.powmod(sum, mod) } % mod end n = input(i) c = input([0] + i[9]) if c.count(&.positive?) == 1 puts min(c) else k = 9 * (1..9).select { |x| c[x] > 0 }.each_combination(2).map { |(i, j)| i - j }.reduce(0) { |x, y| x.gcd y } p min_mod(c, k).gcd(k) end