def solve(io) h, w, k = io.get3 c = io.get_c(h, String) a = Array.new_md(h, w, 0) c.each_with_index do |ci, i| ci.chars.each_with_index do |cij, j| a[i][j] = (1 << (cij - 'a')) end end st = Array.new(h) { |i| SegmentTree.new(a[i]) { |a, b| a | b } } r = 0 h.times do |i| w.times do |j| m = {h - i, w - j}.min f1 = (1..m).bsearch do |b| st[i, b].map { |sti| sti[j, b] }.reduce { |a, b| a | b }.popcount >= k end f2 = (1..m).bsearch do |b| st[i, b].map { |sti| sti[j, b] }.reduce { |a, b| a | b }.popcount > k end r += (f2 || (m + 1)) - (f1 || (m + 1)) end end io.put r end class ProconIO def initialize(@ins : IO = STDIN, @outs : IO = STDOUT) @buf = IO::Memory.new("") end def get(k : T.class = Int32) forall T get_v(k) end macro define_get {% for i in (2..9) %} def get({{ *(1..i).map { |j| "k#{j}".id } }}) { {{ *(1..i).map { |j| "get(k#{j})".id } }} } end {% end %} end define_get macro define_getn {% for i in (2..9) %} def get{{i}}(k : T.class = Int32) forall T get({{ *(1..i).map { "k".id } }}) end {% end %} end define_getn def get_a(n : Int, k : T.class = Int32) forall T Array.new(n) { get_v(k) } end def get_c(n : Int, k : T.class = Int32) forall T get_a(n, k) end macro define_get_c {% for i in (2..9) %} def get_c(n : Int, {{ *(1..i).map { |j| "k#{j}".id } }}) a = Array.new(n) { get({{ *(1..i).map { |j| "k#{j}".id } }}) } { {{ *(1..i).map { |j| "a.map { |e| e[#{j-1}] }".id } }} } end {% end %} end define_get_c macro define_getn_c {% for i in (2..9) %} def get{{i}}_c(n : Int, k : T.class = Int32) forall T get_c(n, {{ *(1..i).map { "k".id } }}) end {% end %} end define_getn_c def get_m(r : Int, c : Int, k : T.class = Int32) forall T Array.new(r) { get_a(c, k) } end macro define_put {% for i in (1..9) %} def put({{ *(1..i).map { |j| "v#{j}".id } }}, *, delimiter = " ") {% for j in (1..i) %} print_v(v{{j}}, delimiter) {% if j < i %}@outs << delimiter{% end %} {% end %} @outs.puts end {% end %} end define_put def put_e(*vs) put(*vs) exit end def put_f(*vs) put(*vs) @outs.flush end private def get_v(k : Int32.class); get_token.to_i32; end private def get_v(k : Int64.class); get_token.to_i64; end private def get_v(k : UInt32.class); get_token.to_u32; end private def get_v(k : UInt64.class); get_token.to_u64; end private def get_v(k : Float64.class); get_token.to_f64; end private def get_v(k : String.class); get_token; end private def get_token loop do token = @buf.gets(' ', chomp: true) break token unless token.nil? @buf = IO::Memory.new(@ins.read_line) end end private def print_v(v, dlimiter) @outs << v end private def print_v(v : Enumerable, delimiter) v.each_with_index do |e, i| @outs << e @outs << delimiter if i < v.size - 1 end end end struct Int def cdiv(b : Int) (self + b - 1) // b end def bit?(i : Int) bit(i) == 1 end def set_bit(i : Int) self | (self.class.new(1) << i) end def reset_bit(i : Int) self & ~(self.class.new(1) << i) end {% if compare_versions(env("CRYSTAL_VERSION") || "0.0.0", "0.34.0") < 0 %} def bit_length : Int32 x = self < 0 ? ~self : self if x.is_a?(Int::Primitive) Int32.new(sizeof(self) * 8 - x.leading_zeros_count) else to_s(2).size end end {% end %} end struct Float64 def near_zero? self.abs < EPSILON end end struct Number {% if compare_versions(env("CRYSTAL_VERSION") || "0.0.0", "1.1.0") < 0 %} def zero? self == 0 end def positive? self > 0 end def negative? self < 0 end {% end %} {% if compare_versions(env("CRYSTAL_VERSION") || "0.0.0", "0.36.0") < 0 %} def self.additive_identity zero end def self.multiplicative_identity new(1) end {% end %} end class Array macro new_md(*args, &block) {% if !block %} {% for arg, i in args[0...-2] %} Array.new({{arg}}) { {% end %} Array.new({{args[-2]}}, {{args[-1]}}) {% for arg in args[0...-2] %} } {% end %} {% else %} {% for arg, i in args %} Array.new({{arg}}) { |_i{{i}}| {% end %} {% for block_arg, i in block.args %} {{block_arg}} = _i{{i}} {% end %} {{block.body}} {% for arg in args %} } {% end %} {% end %} end end module Math {% if compare_versions(env("CRYSTAL_VERSION") || "0.0.0", "1.2.0") < 0 %} def isqrt(value : Int::Primitive) raise ArgumentError.new "Input must be non-negative integer" if value < 0 return value if value < 2 res = value.class.zero bit = res.succ << (res.leading_zeros_count - 2) bit >>= value.leading_zeros_count & ~0x3 while (bit != 0) if value >= res + bit value -= res + bit res = (res >> 1) + bit else res >>= 1 end bit >>= 2 end res end {% end %} end macro min_u(a, b) {{a}} = Math.min({{a}}, {{b}}) end macro max_u(a, b) {{a}} = Math.max({{a}}, {{b}}) end macro zip(a, *b, &block) {{a}}.zip({{*b}}) {{block}} end class SegmentTree(T) def initialize(@n : Int32, @init : T = T.zero, &@compose : (T, T) -> T) @an = 1 << (@n - 1).bit_length @buf = Array.new(@an << 1, @init) propagate_all end def initialize(b : Array(T), @init : T = T.zero, &@compose : (T, T) -> T) @n = b.size @an = 1 << (@n - 1).bit_length @buf = Array.new(@an << 1, @init) @buf[@an, @n] = b propagate_all end def [](i : Int) @buf[i + @an] end def [](start : Int, count : Int) l, r = start + @an, start + count + @an r1 = r2 = @init while l != r if l.odd? r1 = @compose.call(r1, @buf[l]) l += 1 end if r.odd? r -= 1 r2 = @compose.call(@buf[r], r2) end l >>= 1 r >>= 1 end @compose.call(r1, r2) end def [](r : Range) sc = Indexable.range_to_index_and_count(r, @n) raise ArgumentError.new("Invalid range") if sc.nil? self[*sc] end def []=(i : Int, v : T) @buf[i + @an] = v propagate(i + @an) end @an : Int32 @buf : Array(T) private def propagate_all (1...@an).reverse_each do |i| @buf[i] = @compose.call(@buf[i << 1], @buf[i << 1 | 1]) end end private def propagate(i : Int) while (i >>= 1) > 0 @buf[i] = @compose.call(@buf[i << 1], @buf[i << 1 | 1]) end end end solve(ProconIO.new)