import macros;macro ImportExpand(s:untyped):untyped = parseStmt($s[2])
# source: src/cplib/tmpl/sheep.nim
ImportExpand "cplib/tmpl/sheep" <=== "when not declared CPLIB_TMPL_SHEEP:\n    const CPLIB_TMPL_SHEEP* = 1\n    {.warning[UnusedImport]: off.}\n    {.hint[XDeclaredButNotUsed]: off.}\n    import algorithm\n    import sequtils\n    import tables\n    import macros\n    import math\n    import sets\n    import strutils\n    import strformat\n    import sugar\n    import heapqueue\n    import streams\n    import deques\n    import bitops\n    import std/lenientops\n    import options\n    #入力系\n    proc scanf(formatstr: cstring){.header: \"<stdio.h>\", varargs.}\n    proc getchar(): char {.importc: \"getchar_unlocked\", header: \"<stdio.h>\", discardable.}\n    proc ii(): int {.inline.} = scanf(\"%lld\\n\", addr result)\n    proc lii(N: int): seq[int] {.inline.} = newSeqWith(N, ii())\n    proc si(): string {.inline.} =\n        result = \"\"\n        var c: char\n        while true:\n            c = getchar()\n            if c == ' ' or c == '\\n' or c == '\\255':\n                break\n            result &= c\n    \n    # 出力系\n    # 1. 実際の処理を行う proc (openArray を受け取る)\n    proc print_internal(prop: tuple[f: File, sepc: string, endc: string, flush: bool], args: openArray[string]) =\n        for i in 0 ..< args.len:\n            prop.f.write(args[i])\n            if i != args.len - 1:\n                prop.f.write(prop.sepc)\n            else:\n                prop.f.write(prop.endc)\n        if prop.flush:\n            prop.f.flushFile()\n\n    # 2. ユーザーが呼び出すためのインターフェース (varargs を受け取る)\n    proc print*(prop: tuple[f: File, sepc: string, endc: string, flush: bool], args: varargs[string, `$`]) =\n        # varargs は内部では openArray として扱えるので、そのまま渡せる\n        print_internal(prop, args)\n\n    proc print*(args: varargs[string, `$`]) =\n        # こちらも内部用の proc を呼ぶ\n        print_internal((f: stdout, sepc: \" \", endc: \"\\n\", flush: false), args)\n    macro getSymbolName(x: typed): string = x.toStrLit\n    macro debug*(args: varargs[untyped]): untyped =\n        when defined(debug):\n            result = newNimNode(nnkStmtList, args)\n            template prop(e: string = \"\"): untyped = (f: stderr, sepc: \"\", endc: e, flush: true)\n            for i, arg in args:\n                if arg.kind == nnkStrLit:\n                    result.add(quote do: print(prop(), \"\\\"\", `arg`, \"\\\"\"))\n                else:\n                    result.add(quote do: print(prop(\": \"), getSymbolName(`arg`)))\n                    result.add(quote do: print(prop(), `arg`))\n                if i != args.len - 1: result.add(quote do: print(prop(), \", \"))\n                else: result.add(quote do: print(prop(), \"\\n\"))\n        else:\n            return (quote do: discard)\n    #chmin,chmax\n    template `max=`(x, y) = x = max(x, y)\n    template `min=`(x, y) = x = min(x, y)\n    proc chmin[T](x: var T, y: T):bool=\n        if x > y:\n            x = y\n            return true\n        return false\n    proc chmax[T](x: var T, y: T):bool=\n        if x < y:\n            x = y\n            return true\n        return false\n    #bit演算\n    proc `%`*(x: int, y: int): int =\n        result = x mod y\n        if y > 0 and result < 0: result += y\n        if y < 0 and result > 0: result += y\n    proc `//`*(x: int, y: int): int{.inline.} =\n        result = x div y\n        if y > 0 and result * y > x: result -= 1\n        if y < 0 and result * y < x: result -= 1\n    proc `%=`(x: var int, y: int): void = x = x%y\n    proc `//=`(x: var int, y: int): void = x = x//y\n    proc `**`(x: int, y: int): int = x^y\n    proc `**=`(x: var int, y: int): void = x = x^y\n    proc `^`(x: int, y: int): int = x xor y\n    proc `|`(x: int, y: int): int = x or y\n    proc `&`(x: int, y: int): int = x and y\n    proc `>>`(x: int, y: int): int = x shr y\n    proc `<<`(x: int, y: int): int = x shl y\n    proc `~`(x: int): int = not x\n    proc `^=`(x: var int, y: int): void = x = x ^ y\n    proc `&=`(x: var int, y: int): void = x = x & y\n    proc `|=`(x: var int, y: int): void = x = x | y\n    proc `>>=`(x: var int, y: int): void = x = x >> y\n    proc `<<=`(x: var int, y: int): void = x = x << y\n    proc `[]`(x: int, n: int): bool = (x and (1 shl n)) != 0\n    #便利な変換\n    proc `!`(x: char, a = '0'): int = int(x)-int(a)\n    #定数\n    when not declared CPLIB_UTILS_CONSTANTS:\n        const CPLIB_UTILS_CONSTANTS* = 1\n        const INF32*: int32 = 1001000027.int32\n        const INF64*: int = int(3300300300300300491)\n    \n    const INF = INF64\n    #converter\n\n    #range\n    iterator range(start: int, ends: int, step: int): int =\n        var i = start\n        if step < 0:\n            while i > ends:\n                yield i\n                i += step\n        elif step > 0:\n            while i < ends:\n                yield i\n                i += step\n    iterator range(ends: int): int = (for i in 0..<ends: yield i)\n    iterator range(start: int, ends: int): int = (for i in\n            start..<ends: yield i)\n\n    #joinが非stringでめちゃくちゃ遅いやつのパッチ\n    proc join*[T: not string](a: openArray[T], sep: string = \"\"): string = a.mapit($it).join(sep)\n\n    proc dump[T](arr:seq[seq[T]])=\n        for i in 0..<len(arr):\n            echo arr[i]\n\n    proc sum(slice:HSlice[int,int]):int=\n        return (slice.a+slice.b)*len(slice)//2\n    \n    proc `<`[T](l,r:seq[T]):bool=\n        for i in 0..<min(len(l),len(r)):\n            if l[i] > r[i]:\n                return false\n            elif l[i] < r[i]:\n                return true\n        return len(l) < len(r)\n    \n    # Yes/No\n    proc yes*(b: bool = true): void = print(if b: \"Yes\" else: \"No\")\n    proc oo*(b: bool = true): void = yes(not b)\n\n    proc takahashi(b:bool = true) : void = print(if b: \"Takahashi\" else: \"Aoki\")\n    proc aoki(b:bool = true) : void = takahashi(not b)\n\n    template dblock(body: untyped) =\n        when defined(debug):\n            body\n"
# source: src/atcoder/modint.nim
ImportExpand "atcoder/modint" <=== "when not declared ATCODER_MODINT_HPP:\n  const ATCODER_MODINT_HPP* = 1\n  import std/macros\n  when not declared ATCODER_GENERATE_DEFINITIONS_NIM:\n    const ATCODER_GENERATE_DEFINITIONS_NIM* = 1\n    import std/macros\n  \n    type hasInv* = concept x\n      x.inv()\n  \n    template generateDefinitions*(name, l, r, typeObj, typeBase, body: untyped): untyped {.dirty.} =\n      proc name*(l, r: typeObj): auto {.inline.} =\n        type T = l.type\n        body\n      proc name*(l: typeBase; r: typeObj): auto {.inline.} =\n        type T = r.type\n        body\n      proc name*(l: typeObj; r: typeBase): auto {.inline.} =\n        type T = l.type\n        body\n  \n    template generatePow*(name) {.dirty.} =\n      proc pow*(m: name; p: SomeInteger): name {.inline.} =\n        when name is hasInv:\n          if p < 0: return pow(m.inv(), -p)\n        else:\n          doAssert p >= 0\n        if (p.type)(0) <= p:\n          var\n            p = p.uint\n            m = m\n          result = m.unit()\n          while p > 0'u:\n            if (p and 1'u) != 0'u: result *= m\n            m *= m\n            p = p shr 1'u\n      proc `^`*[T:name](m: T; p: SomeInteger): T {.inline.} = m.pow(p)\n  \n    macro generateConverter*(name, from_type, to_type) =\n      let fname = ident(\"to\" & $`name` & \"OfGenerateConverter\")\n      quote do:\n        type `name`* = `to_type`\n        converter `fname`*(a:`from_type`):`name` {.used.} =\n          `name`.init(a)\n  \n\n  type\n    StaticModInt*[M: static[int]] = object\n      a:uint32\n    DynamicModInt*[T: static[int]] = object\n      a:uint32\n\n  type ModInt* = StaticModInt or DynamicModInt\n#  type ModInt* = concept x, type T\n#    T is StaticModInt or T is DynamicModInt\n\n  proc isStaticModInt*(T:typedesc[ModInt]):bool = T is StaticModInt\n  proc isDynamicModInt*(T:typedesc[ModInt]):bool = T is DynamicModInt\n  #proc isModInt*(T:typedesc):bool = T.isStaticModInt or T.isDynamicModInt\n  proc isStatic*(T:typedesc[ModInt]):bool = T is StaticModInt\n  proc getMod*[M:static[int]](t:typedesc[StaticModInt[M]]):int {.inline.} = M\n\n\n  when not declared ATCODER_INTERNAL_MATH_HPP:\n    const ATCODER_INTERNAL_MATH_HPP* = 1\n    import std/math\n  \n    # Fast moduler by barrett reduction\n    # Reference: https:#en.wikipedia.org/wiki/Barrett_reduction\n    # NOTE: reconsider after Ice Lake\n    type Barrett* = object\n      m*, im*:uint\n  \n    # @param m `1 <= m`\n    proc initBarrett*(m:uint):auto = Barrett(m:m, im:cast[uint](-1) div m + 1)\n  \n    # @return m\n    proc umod*(self: Barrett):uint =\n      self.m\n  \n    {.emit: \"\"\"\n  #include<cstdio>\n  inline unsigned long long calc_mul(const unsigned long long &a, const unsigned long long &b){\n    return (unsigned long long)(((unsigned __int128)(a)*b) >> 64);\n  }\n  \"\"\".}\n    proc calc_mul*(a,b:culonglong):culonglong {.importcpp: \"calc_mul(#,#)\", nodecl, inline.}\n    # @param a `0 <= a < m`\n    # @param b `0 <= b < m`\n    # @return `a * b % m`\n    proc quo*(self: Barrett, n:int | uint):int =\n      let n = n.uint\n      let x = calc_mul(n.culonglong, self.im.culonglong).uint\n      let r = n - x * self.m\n      return int(if self.m <= r: x - 1 else: x)\n    proc rem*(self: Barrett, n:int | uint):int =\n      let n = n.uint\n      let x = calc_mul(n.culonglong, self.im.culonglong).uint\n      let r = n - x * self.m\n      return int(if self.m <= r: r + self.m else: r)\n    proc quorem*(self: Barrett, n:int | uint):(int, int) =\n      let n = n.uint\n      let x = calc_mul(n.culonglong, self.im.culonglong).uint\n      let r = n - x * self.m\n      return if self.m <= r: (int(x - 1), int(r + self.m)) else: (int(x), int(r))\n  \n    proc pow*(self: Barrett, n:uint | int, p:int):int =\n      var\n        a = self.rem(n)\n        r:uint = if self.m == 1: 0 else: 1\n        p = p\n      while p > 0:\n        if (p and 1) != 0: r = self.mul(r, a.uint)\n        a = self.mul(a.uint, a.uint).int\n        p = p shr 1\n      return int(r)\n  \n    proc mul*(self: Barrett, a:uint, b:uint):uint {.inline.} =\n      # [1] m = 1\n      # a = b = im = 0, so okay\n  \n      # [2] m >= 2\n      # im = ceil(2^64 / m)\n      # -> im * m = 2^64 + r (0 <= r < m)\n      # let z = a*b = c*m + d (0 <= c, d < m)\n      # a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im\n      # c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2\n      # ((ab * im) >> 64) == c or c + 1\n      let z = a * b\n      #  #ifdef _MSC_VER\n      #      unsigned long long x;\n      #      _umul128(z, im, &x);\n      #  #else\n      #      unsigned long long x =\n      #        (unsigned long long)(((unsigned __int128)(z)*im) >> 64);\n      #  #endif\n      #let x = calc_mul(z.culonglong, self.im.culonglong).uint\n      #result = z - x * self.m\n      #if self.m <= result: result += self.m\n      return self.rem(z).uint\n  \n    # @param n `0 <= n`\n    # @param m `1 <= m`\n    # @return `(x ** n) % m`\n    proc pow_mod_constexpr*(x, n, m:int):int =\n      if m == 1: return 0\n      var\n        r = 1\n        y = floorMod(x, m)\n        n = n\n      while n != 0:\n        if (n and 1) != 0: r = (r * y) mod m\n        y = (y * y) mod m\n        n = n shr 1\n      return r.int\n    \n    # Reference:\n    # M. Forisek and J. Jancina,\n    # Fast Primality Testing for Integers That Fit into a Machine Word\n    # @param n `0 <= n`\n    proc is_prime_constexpr*(n:int):bool =\n      if n <= 1: return false\n      if n == 2 or n == 7 or n == 61: return true\n      if n mod 2 == 0: return false\n      var d = n - 1\n      while d mod 2 == 0: d = d div 2\n      for a in [2, 7, 61]:\n        var\n          t = d\n          y = pow_mod_constexpr(a, t, n)\n        while t != n - 1 and y != 1 and y != n - 1:\n          y = y * y mod n\n          t =  t shl 1\n        if y != n - 1 and t mod 2 == 0:\n          return false\n      return true\n    proc is_prime*[n:static[int]]():bool = is_prime_constexpr(n)\n  #  \n  #  # @param b `1 <= b`\n  #  # @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g\n    proc inv_gcd*(a, b:int):(int,int) =\n      var a = floorMod(a, b)\n      if a == 0: return (b, 0)\n    \n      # Contracts:\n      # [1] s - m0 * a = 0 (mod b)\n      # [2] t - m1 * a = 0 (mod b)\n      # [3] s * |m1| + t * |m0| <= b\n      var\n        s = b\n        t = a\n        m0 = 0\n        m1 = 1\n    \n      while t != 0:\n        var u = s div t\n        s -= t * u;\n        m0 -= m1 * u;  # |m1 * u| <= |m1| * s <= b\n    \n        # [3]:\n        # (s - t * u) * |m1| + t * |m0 - m1 * u|\n        # <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)\n        # = s * |m1| + t * |m0| <= b\n    \n        var tmp = s\n        s = t;t = tmp;\n        tmp = m0;m0 = m1;m1 = tmp;\n      # by [3]: |m0| <= b/g\n      # by g != b: |m0| < b/g\n      if m0 < 0: m0 += b div s\n      return (s, m0)\n  \n    # Compile time primitive root\n    # @param m must be prime\n    # @return primitive root (and minimum in now)\n    proc primitive_root_constexpr*(m:int):int =\n      if m == 2: return 1\n      if m == 167772161: return 3\n      if m == 469762049: return 3\n      if m == 754974721: return 11\n      if m == 998244353: return 3\n      var divs:array[20, int]\n      divs[0] = 2\n      var cnt = 1\n      var x = (m - 1) div 2\n      while x mod 2 == 0: x = x div 2\n      var i = 3\n      while i * i <= x:\n        if x mod i == 0:\n          divs[cnt] = i\n          cnt.inc\n          while x mod i == 0:\n            x = x div i\n        i += 2\n      if x > 1:\n        divs[cnt] = x\n        cnt.inc\n      var g = 2\n      while true:\n        var ok = true\n        for i in 0..<cnt:\n          if pow_mod_constexpr(g, (m - 1) div divs[i], m) == 1:\n            ok = false\n            break\n        if ok: return g\n        g.inc\n    proc primitive_root*[m:static[int]]():auto =\n      primitive_root_constexpr(m)\n  \n    # @param n `n < 2^32`\n    # @param m `1 <= m < 2^32`\n    # @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)\n    proc floor_sum_unsigned*(n, m, a, b:uint):uint =\n      result = 0\n      var (n, m, a, b) = (n, m, a, b)\n      while true:\n        if a >= m:\n          result += n * (n - 1) div 2 * (a div m)\n          a = a mod m\n        if b >= m:\n          result += n * (b div m)\n          b = b mod m\n  \n        let y_max = a * n + b\n        if y_max < m: break\n        # y_max < m * (n + 1)\n        # floor(y_max / m) <= n\n        n = y_max div m\n        b = y_max mod m\n        swap(m, a)\n  \n\n  proc getBarrett*[T:static[int]](t:typedesc[DynamicModInt[T]]):ptr Barrett =\n    {.cast(noSideEffect).}:\n      var Barrett_of_DynamicModInt {.global.} = initBarrett(998244353.uint)\n      return Barrett_of_DynamicModInt.addr\n  \n  proc getMod*[T:static[int]](t:typedesc[DynamicModInt[T]]):uint32 {.inline.} =\n    (t.getBarrett)[].m.uint32\n  proc setMod*[T:static[int]](t:typedesc[DynamicModInt[T]], M:SomeInteger){.inline.} =\n    (t.getBarrett)[] = initBarrett(M.uint)\n\n  proc val*(m: ModInt): int {.inline.} = int(m.a)\n\n  proc `$`*(m: StaticModInt or DynamicModInt): string {.inline.} = $(m.val())\n\n  template umod*[T:ModInt](self: typedesc[T] or T):uint32 =\n    when T is typedesc:\n      when T is StaticModInt:\n        T.M.uint32\n      elif T is DynamicModInt:\n        T.getMod()\n      else:\n        static: assert false\n    else: T.umod\n\n  template `mod`*[T:ModInt](self:typedesc[T] or T):int = T.umod.int\n\n  proc init*[T:ModInt](t:typedesc[T], v: SomeInteger or T): auto {.inline.} =\n    when v is T: return v\n    else:\n      when v is SomeUnsignedInt:\n        if v.uint < T.umod:\n          return T(a:v.uint32)\n        else:\n          return T(a:(v.uint mod T.umod.uint).uint32)\n      else:\n        var v = v.int\n        if 0 <= v:\n          if v < T.mod: return T(a:v.uint32)\n          else: return T(a:(v mod T.mod).uint32)\n        else:\n          v = v mod T.mod\n          if v < 0: v += T.mod\n          return T(a:v.uint32)\n  proc unit*[T:ModInt](t:typedesc[T] or T):T = T.init(1)\n\n  template initModInt*(v: SomeInteger or ModInt; M: static[int] = 1_000_000_007): auto =\n    StaticModInt[M].init(v)\n\n# TODO\n#  converter toModInt[M:static[int]](n:SomeInteger):StaticModInt[M] {.inline.} = initModInt(n, M)\n\n#  proc initModIntRaw*(v: SomeInteger; M: static[int] = 1_000_000_007): auto {.inline.} =\n#    ModInt[M](v.uint32)\n  proc raw*[T:ModInt](t:typedesc[T], v:SomeInteger):auto = T(a:v)\n\n  proc inv*[T:ModInt](v:T):T {.inline.} =\n    var\n      a = v.a.int\n      b = T.mod\n      u = 1\n      v = 0\n    while b > 0:\n      let t = a div b\n      a -= t * b;swap(a, b)\n      u -= t * v;swap(u, v)\n    return T.init(u)\n\n\n  proc `-`*[T:ModInt](m: T): T {.inline.} =\n    if int(m.a) == 0: return m\n    else: return T(a:m.umod() - m.a)\n\n  proc `+=`*[T:ModInt](m: var T; n: SomeInteger | T):T {.inline discardable.} =\n    m.a += T.init(n).a\n    if m.a >= T.umod: m.a -= T.umod\n    return m\n\n  proc `-=`*[T:ModInt](m: var T; n: SomeInteger | T):T {.inline discardable.} =\n    m.a -= T.init(n).a\n    if m.a >= T.umod: m.a += T.umod\n    return m\n\n  proc `*=`*[T:ModInt](m: var T; n: SomeInteger | T):T {.inline discardable.} =\n    when T is StaticModInt:\n      m.a = (m.a.uint * T.init(n).a.uint mod T.umod).uint32\n    elif T is DynamicModInt:\n      m.a = T.getBarrett[].mul(m.a.uint, T.init(n).a.uint).uint32\n    else:\n      static: assert false\n    return m\n\n  proc `/=`*[T:ModInt](m: var T; n: SomeInteger | T):T {.inline discardable.} =\n    m.a = (m.a.uint * T.init(n).inv().a.uint mod T.umod).uint32\n    return m\n\n  generateDefinitions(`+`, m, n, ModInt, SomeInteger):\n    result = T.init(m)\n    result += n\n\n  generateDefinitions(`-`, m, n, ModInt, SomeInteger):\n    result = T.init(m)\n    result -= n\n\n  generateDefinitions(`*`, m, n, ModInt, SomeInteger):\n    result = T.init(m)\n    result *= n\n\n  generateDefinitions(`/`, m, n, ModInt, SomeInteger):\n    result = T.init(m)\n    result /= n\n\n  generateDefinitions(`==`, m, n, ModInt, SomeInteger):\n    result = (T.init(m).val() == T.init(n).val())\n\n  proc inc*(m: var ModInt):ModInt {.inline discardable.} =\n    m.a.inc\n    if m.a == m.umod.uint32:\n      m.a = 0\n    return m\n  proc `++`*(m: var ModInt):ModInt {.inline discardable.} = m.inc\n\n  proc dec*(m: var ModInt):ModInt {.inline discardable.} =\n    if m.a == 0.uint32:\n      m.a = m.umod - 1\n    else:\n      m.a.dec\n    return m\n  proc `--`*(m: var ModInt):ModInt {.inline discardable.} = m.dec\n\n  generatePow(ModInt)\n  \n  # TODO: intのところはSomeIntegerに拡張したいがそうするとSystem.nimのuintのconverterとバッティングする。。。\n  template useStaticModint*(name, M) =\n    generateConverter(name, int, StaticModInt[M])\n  template useDynamicModInt*(name, M) =\n    generateConverter(name, int, DynamicModInt[M])\n\n  # TODO: Nimのstatic[int]を使うconverterがバグっていて個々に宣言しないとconverterが使えない\n  # したがって、下記以外のmodintを使う場合はuseStaticModIntあるいはuseDynamicModIntで宣言が必要\n  useStaticModInt(modint998244353, 998244353)\n  useStaticModInt(modint1000000007, 1000000007)\n  useDynamicModInt(modint, -1)\n\n  import std/math as math_lib_modint\n  proc estimateRational*(a:ModInt, ub:int = int(sqrt(float(ModInt.mod))), output_stderr:static[bool] = false):string =\n    var v:seq[tuple[s, n, d: int]]\n    for d in 1 .. ub:\n      var n = (a * d).val\n      # n or mod - n\n      if n * 2 > a.mod:\n        n = - (a.mod - n)\n      if gcd(n, d) > 1: continue\n      v.add((n.abs + d, n, d))\n    v.sort\n    when output_stderr:\n      stderr.write \"estimation result: \", v\n    return $v[0].n & \"/\" & $v[0].d\n\n  # TODO:\n  # Modint -> intのconverterあるとmint(2) * 3みたいなのがintになっちゃう\n  # converter toInt*(m: ModInt):int {.inline.} = m.val\n\n\n"
# source: src/cplib/graph/graph.nim
ImportExpand "cplib/graph/graph" <=== "when not declared CPLIB_GRAPH_GRAPH:\n    const CPLIB_GRAPH_GRAPH* = 1\n\n    import sequtils\n    import math\n    type DynamicGraph*[T] = ref object of RootObj\n        edges*: seq[seq[(int32, T)]]\n        len*: int\n    type StaticGraph*[T] = ref object of RootObj\n        src*, dst*: seq[int32]\n        cost*: seq[T]\n        elist*: seq[(int32, T)]\n        start*: seq[int32]\n        len*: int\n\n    type WeightedDirectedGraph*[T] = ref object of DynamicGraph[T]\n    type WeightedUnDirectedGraph*[T] = ref object of DynamicGraph[T]\n    type UnWeightedDirectedGraph* = ref object of DynamicGraph[int]\n    type UnWeightedUnDirectedGraph* = ref object of DynamicGraph[int]\n    type WeightedDirectedStaticGraph*[T] = ref object of StaticGraph[T]\n    type WeightedUnDirectedStaticGraph*[T] = ref object of StaticGraph[T]\n    type UnWeightedDirectedStaticGraph* = ref object of StaticGraph[int]\n    type UnWeightedUnDirectedStaticGraph* = ref object of StaticGraph[int]\n\n    type GraphTypes*[T] = DynamicGraph[T] or StaticGraph[T]\n    type DirectedGraph* = WeightedDirectedGraph or UnWeightedDirectedGraph or WeightedDirectedStaticGraph or UnWeightedDirectedStaticGraph\n    type UnDirectedGraph* = WeightedUnDirectedGraph or UnWeightedUnDirectedGraph or WeightedUnDirectedStaticGraph or UnWeightedUnDirectedStaticGraph\n    type WeightedGraph*[T] = WeightedDirectedGraph[T] or WeightedUnDirectedGraph[T] or WeightedDirectedStaticGraph[T] or WeightedUnDirectedStaticGraph[T]\n    type UnWeightedGraph* = UnWeightedDirectedGraph or UnWeightedUnDirectedGraph or UnWeightedDirectedStaticGraph or UnWeightedUnDirectedStaticGraph\n    type DynamicGraphTypes* = WeightedDirectedGraph or UnWeightedDirectedGraph or WeightedUnDirectedGraph or UnWeightedUnDirectedGraph\n    type StaticGraphTypes* = WeightedDirectedStaticGraph or UnWeightedDirectedStaticGraph or WeightedUnDirectedStaticGraph or UnWeightedUnDirectedStaticGraph\n\n    proc add_edge_dynamic_impl*[T](g: DynamicGraph[T], u, v: int, cost: T, directed: bool) =\n        g.edges[u].add((v.int32, cost))\n        if not directed: g.edges[v].add((u.int32, cost))\n\n    proc initWeightedDirectedGraph*(N: int, edgetype: typedesc = int): WeightedDirectedGraph[edgetype] =\n        result = WeightedDirectedGraph[edgetype](edges: newSeq[seq[(int32, edgetype)]](N), len: N)\n    proc add_edge*[T](g: var WeightedDirectedGraph[T], u, v: int, cost: T) =\n        g.add_edge_dynamic_impl(u, v, cost, true)\n\n    proc initWeightedUnDirectedGraph*(N: int, edgetype: typedesc = int): WeightedUnDirectedGraph[edgetype] =\n        result = WeightedUnDirectedGraph[edgetype](edges: newSeq[seq[(int32, edgetype)]](N), len: N)\n    proc add_edge*[T](g: var WeightedUnDirectedGraph[T], u, v: int, cost: T) =\n        g.add_edge_dynamic_impl(u, v, cost, false)\n\n    proc initUnWeightedDirectedGraph*(N: int): UnWeightedDirectedGraph =\n        result = UnWeightedDirectedGraph(edges: newSeq[seq[(int32, int)]](N), len: N)\n    proc add_edge*(g: var UnWeightedDirectedGraph, u, v: int) =\n        g.add_edge_dynamic_impl(u, v, 1, true)\n\n    proc initUnWeightedUnDirectedGraph*(N: int): UnWeightedUnDirectedGraph =\n        result = UnWeightedUnDirectedGraph(edges: newSeq[seq[(int32, int)]](N), len: N)\n    proc add_edge*(g: var UnWeightedUnDirectedGraph, u, v: int) =\n        g.add_edge_dynamic_impl(u, v, 1, false)\n\n    proc len*[T](G: WeightedGraph[T]): int = G.len\n    proc len*(G: UnWeightedGraph): int = G.len\n\n    iterator `[]`*[T](g: WeightedDirectedGraph[T] or WeightedUnDirectedGraph[T], x: int): (int, T) =\n        for e in g.edges[x]: yield (e[0].int, e[1])\n    iterator `[]`*(g: UnWeightedDirectedGraph or UnWeightedUnDirectedGraph, x: int): int =\n        for e in g.edges[x]: yield e[0].int\n\n    proc add_edge_static_impl*[T](g: StaticGraph[T], u, v: int, cost: T, directed: bool) =\n        g.src.add(u.int32)\n        g.dst.add(v.int32)\n        g.cost.add(cost)\n        if not directed:\n            g.src.add(v.int32)\n            g.dst.add(u.int32)\n            g.cost.add(cost)\n\n    proc build_impl*[T](g: StaticGraph[T]) =\n        g.start = newSeqWith(g.len + 1, 0.int32)\n        for i in 0..<g.src.len:\n            g.start[g.src[i]] += 1\n        g.start.cumsum\n        g.elist = newSeq[(int32, T)](g.start[^1])\n        for i in countdown(g.src.len - 1, 0):\n            var u = g.src[i]\n            var v = g.dst[i]\n            g.start[u] -= 1\n            g.elist[g.start[u]] = (v, g.cost[i])\n    proc build*(g: StaticGraphTypes) = g.build_impl()\n\n    proc initWeightedDirectedStaticGraph*(N: int, edgetype: typedesc = int, capacity: int = 0): WeightedDirectedStaticGraph[edgetype] =\n        result = WeightedDirectedStaticGraph[edgetype](\n            src: newSeqOfCap[int32](capacity),\n            dst: newSeqOfCap[int32](capacity),\n            cost: newSeqOfCap[edgetype](capacity),\n            elist: newSeq[(int32, edgetype)](0),\n            start: newSeq[int32](0),\n            len: N\n        )\n    proc add_edge*[T](g: var WeightedDirectedStaticGraph[T], u, v: int, cost: T) =\n        g.add_edge_static_impl(u, v, cost, true)\n\n    proc initWeightedUnDirectedStaticGraph*(N: int, edgetype: typedesc = int, capacity: int = 0): WeightedUnDirectedStaticGraph[edgetype] =\n        result = WeightedUnDirectedStaticGraph[edgetype](\n            src: newSeqOfCap[int32](capacity*2),\n            dst: newSeqOfCap[int32](capacity*2),\n            cost: newSeqOfCap[edgetype](capacity*2),\n            elist: newSeq[(int32, edgetype)](0),\n            start: newSeq[int32](0),\n            len: N\n        )\n    proc add_edge*[T](g: var WeightedUnDirectedStaticGraph[T], u, v: int, cost: T) =\n        g.add_edge_static_impl(u, v, cost, false)\n\n    proc initUnWeightedDirectedStaticGraph*(N: int, capacity: int = 0): UnWeightedDirectedStaticGraph =\n        result = UnWeightedDirectedStaticGraph(\n            src: newSeqOfCap[int32](capacity),\n            dst: newSeqOfCap[int32](capacity),\n            cost: newSeqOfCap[int](capacity),\n            elist: newSeq[(int32, int)](0),\n            start: newSeq[int32](0),\n            len: N\n        )\n    proc add_edge*(g: var UnWeightedDirectedStaticGraph, u, v: int) =\n        g.add_edge_static_impl(u, v, 1, true)\n\n    proc initUnWeightedUnDirectedStaticGraph*(N: int, capacity: int = 0): UnWeightedUnDirectedStaticGraph =\n        result = UnWeightedUnDirectedStaticGraph(\n            src: newSeqOfCap[int32](capacity*2),\n            dst: newSeqOfCap[int32](capacity*2),\n            cost: newSeqOfCap[int](capacity*2),\n            elist: newSeq[(int32, int)](0),\n            start: newSeq[int32](0),\n            len: N\n        )\n    proc add_edge*(g: var UnWeightedUnDirectedStaticGraph, u, v: int) =\n        g.add_edge_static_impl(u, v, 1, false)\n\n    proc static_graph_initialized_check*[T](g: StaticGraph[T]) = assert g.start.len > 0, \"Static Graph must be initialized before use.\"\n\n    iterator `[]`*[T](g: WeightedDirectedStaticGraph[T] or WeightedUnDirectedStaticGraph[T], x: int): (int, T) =\n        g.static_graph_initialized_check()\n        for i in g.start[x]..<g.start[x+1]: yield (g.elist[i][0].int, g.elist[i][1])\n    iterator `[]`*(g: UnWeightedDirectedStaticGraph or UnWeightedUnDirectedStaticGraph, x: int): int =\n        g.static_graph_initialized_check()\n        for i in g.start[x]..<g.start[x+1]: yield g.elist[i][0].int\n\n    iterator to_and_cost*[T](g: DynamicGraph[T], x: int): (int, T) =\n        for e in g.edges[x]: yield (e[0].int, e[1])\n    iterator to_and_cost*[T](g: StaticGraph[T], x: int): (int, T) =\n        g.static_graph_initialized_check()\n        for i in g.start[x]..<g.start[x+1]: yield (g.elist[i][0].int, g.elist[i][1])\n    \n    import tables\n\n    type UnWeightedUnDirectedTableGraph*[T] = object \n        toi* : Table[T,int]\n        v* : seq[T]\n        graph* : UnWeightedUnDirectedGraph\n\n    type UnWeightedDirectedTableGraph*[T] = object \n        toi* : Table[T,int]\n        v* : seq[T]\n        graph* : UnWeightedDirectedGraph\n\n    type WeightedUnDirectedTableGraph*[T,S] = object \n        toi* : Table[T,int]\n        v* : seq[T]\n        graph* : WeightedUnDirectedGraph[S]\n\n    type WeightedDirectedTableGraph*[T,S] = object \n        toi* : Table[T,int]\n        v* : seq[T]\n        graph* : WeightedDirectedGraph[S]\n\n    type UnWeightedTableGraph*[T] = UnWeightedUnDirectedTableGraph[T] or UnWeightedDirectedTableGraph[T]\n    type WeightedTableGraph*[T,S] = WeightedUnDirectedTableGraph[T,S] or WeightedDirectedTableGraph[T,S]\n\n    proc initUnWeightedUnDirectedTableGraph*[T](V:seq[T]):UnWeightedUnDirectedTableGraph[T]=\n        for i in 0..<len(V):\n            result.toi[V[i]] = i\n        result.graph = initUnWeightedUnDirectedGraph(len(V))\n        result.v = V\n\n    proc initUnWeightedDirectedTableGraph*[T](V:seq[T]):UnWeightedDirectedTableGraph[T]=\n        for i in 0..<len(V):\n            result.toi[V[i]] = i\n        result.graph = initUnWeightedDirectedGraph(len(V))\n        result.v = V\n\n    proc initWeightedUnDirectedTableGraph*[T](V:seq[T],S:typedesc = int):WeightedUnDirectedTableGraph[T,S]=\n        for i in 0..<len(V):\n            result.toi[V[i]] = i\n        result.graph = initWeightedUnDirectedGraph(len(V),S)\n        result.v = V\n\n    proc initWeightedDirectedTableGraph*[T](V:seq[T],S:typedesc = int):WeightedDirectedTableGraph[T,S]=\n        for i in 0..<len(V):\n            result.toi[V[i]] = i\n        result.graph = initWeightedDirectedGraph(len(V),S)\n        result.v = V\n\n    proc add_edge*[T](g: var UnWeightedTableGraph[T],u,v:int)=\n        g.graph.add_edge(g.toi[u],g.toi[v])\n\n    proc add_edge*[T,S](g: var WeightedTableGraph[T,S],u,v:int,cost:S)=\n        g.graph.add_edge(g.toi[u],g.toi[v],cost)\n\n    iterator `[]`*[T,S](g: WeightedDirectedTableGraph[T,S] or WeightedUnDirectedTableGraph[T,S], x: T): (T, S) = \n        for (x,y) in g.graph[g.toi[x]]:\n            yield (g.v[x],y)\n    iterator `[]`*[T](g: UnWeightedDirectedTableGraph[T] or UnWeightedUnDirectedTableGraph[T], x: T): T = \n        for x in g.graph[g.toi[x]]:\n            yield g.v[x]\n\n"
# source: src/cplib/tree/heavylightdecomposition.nim
ImportExpand "cplib/tree/heavylightdecomposition" <=== "when not declared CPLIB_TREE_HLD:\n    const CPLIB_TREE_HLD* = 1\n    import sequtils\n    import algorithm\n    import sets\n    # https://atcoder.jp/contests/abc337/submissions/50216964\n    # ↑上記の提出より引用\n    type HeavyLightDecomposition* = ref object \n        N*: int\n        P*, PP*, PD*, D*, I*, rangeL*, rangeR*: seq[int]\n    proc initHld*(g: UnDirectedGraph, root: int): HeavyLightDecomposition =\n        var hld = HeavyLightDecomposition()\n        var n: int = g.len\n        hld.N = n\n        hld.P = newSeqWith(n, -1)\n        hld.I = newSeqWith(n, 0)\n        hld.I[0] = root\n        var iI = 1\n        for i in 0..<n:\n            var p = hld.I[i]\n            for e in g[p]:\n                if hld.P[p] != e:\n                    hld.I[iI] = e\n                    hld.P[e] = p\n                    iI += 1\n        var Z = newSeqWith(n, 1)\n        var nx = newSeqWith(n, -1)\n        hld.PP = newSeqWith(n, 0)\n        for i in 0..<n:\n            hld.PP[i] = i\n        for i in 1..<n:\n            var p = hld.I[n-i]\n            Z[hld.P[p]] += Z[p]\n            if nx[hld.P[p]] == -1 or Z[nx[hld.P[p]]] < Z[p]:\n                nx[hld.P[p]] = p\n        for p in hld.I:\n            if nx[p] != -1:\n                hld.PP[nx[p]] = p\n        hld.PD = newSeqWith(n, n)\n        hld.PD[root] = 0\n        hld.D = newSeqWith(n, 0)\n        for p in hld.I:\n            if p != root:\n                hld.PP[p] = hld.PP[hld.PP[p]]\n                hld.PD[p] = min(hld.PD[hld.PP[p]], hld.PD[hld.P[p]]+1)\n                hld.D[p] = hld.D[hld.P[p]]+1\n        hld.rangeL = newSeqWith(n, 0)\n        hld.rangeR = newSeqWith(n, 0)\n        for p in hld.I:\n            hld.rangeR[p] = hld.rangeL[p] + Z[p]\n            var ir = hld.rangeR[p]\n            for e in g[p]:\n                if hld.P[p] != e and e != nx[p]:\n                    ir -= Z[e]\n                    hld.rangeL[e] = ir\n            if nx[p] != -1:\n                hld.rangeL[nx[p]] = hld.rangeL[p] + 1\n        for i in 0..<n:\n            hld.I[hld.rangeL[i]] = i\n        return hld\n    proc initHld*(g: DirectedGraph, root: int): HeavyLightDecomposition =\n        var n = g.len\n        var gn = initUnWeightedUnDirectedStaticGraph(n)\n        var seen = initHashSet[(int, int)]()\n        for i in 0..<n:\n            for (j, _) in g[i]:\n                if (i, j) notin seen:\n                    gn.add_edge(i, j)\n                    seen.incl((i, j))\n                    seen.incl((j, i))\n        gn.build\n        return initHld(gn, root)\n    proc initHld*(adj: seq[seq[int]], root: int): HeavyLightDecomposition =\n        var n = adj.len\n        var gn = initUnWeightedUnDirectedStaticGraph(n)\n        var seen = initHashSet[(int, int)]()\n        for i in 0..<n:\n            for j in adj[i]:\n                if (i, j) notin seen:\n                    gn.add_edge(i, j)\n                    seen.incl((i, j))\n                    seen.incl((j, i))\n        gn.build\n        return initHld(gn, root)\n    proc numVertices*(hld: HeavyLightDecomposition): int = hld.N\n    proc depth*(hld: HeavyLightDecomposition, p: int): int = hld.D[p]\n    proc toSeq*(hld: HeavyLightDecomposition, vtx: int): int = hld.rangeL[vtx]\n    proc toVtx*(hld: HeavyLightDecomposition, seqidx: int): int = hld.I[seqidx]\n    proc toSeq2In*(hld: HeavyLightDecomposition, vtx: int): int = hld.rangeL[vtx] * 2 - hld.D[vtx]\n    proc toSeq2Out*(hld: HeavyLightDecomposition, vtx: int): int = hld.rangeR[vtx] * 2 - hld.D[vtx] - 1\n    proc parentOf*(hld: HeavyLightDecomposition, v: int): int = hld.P[v]\n    proc heavyRootOf*(hld: HeavyLightDecomposition, v: int): int = hld.PP[v]\n    proc heavyChildOf*(hld: HeavyLightDecomposition, v: int): int =\n        if hld.toSeq(v) == hld.N-1:\n            return -1\n        var cand = hld.toVtx(hld.toSeq(v) + 1)\n        if hld.PP[v] == hld.PP[cand]:\n            return cand\n        -1\n    proc lca*(hld: HeavyLightDecomposition, u: int, v: int): int =\n        var (u, v) = (u, v)\n        if hld.PD[u] < hld.PD[v]:\n            swap(u, v)\n        while hld.PD[u] > hld.PD[v]:\n            u = hld.P[hld.PP[u]]\n        while hld.PP[u] != hld.PP[v]:\n            u = hld.P[hld.PP[u]]\n            v = hld.P[hld.PP[v]]\n        if hld.D[u] > hld.D[v]:\n            return v\n        u\n    proc dist*(hld: HeavyLightDecomposition, u: int, v: int): int =\n        hld.depth(u) + hld.depth(v) - hld.depth(hld.lca(u, v)) * 2\n    proc path*(hld: HeavyLightDecomposition, r: int, c: int, include_root: bool, reverse_path: bool): seq[(int, int)] =\n        var (r, c) = (r, c)\n        var k = hld.PD[c] - hld.PD[r] + 1\n        if k <= 0:\n            return @[]\n        var res = newSeqWith(k, (0, 0))\n        for i in 0..<k-1:\n            res[i] = (hld.rangeL[hld.PP[c]], hld.rangeL[c] + 1)\n            c = hld.P[hld.PP[c]]\n        if hld.PP[r] != hld.PP[c] or hld.D[r] > hld.D[c]:\n            return @[]\n        var root_off = int(not include_root)\n        res[^1] = (hld.rangeL[r]+root_off, hld.rangeL[c]+1)\n        if res[^1][0] == res[^1][1]:\n            discard res.pop()\n            k -= 1\n        if reverse_path:\n            for i in 0..<k:\n                res[i] = (hld.N - res[i][1], hld.N - res[i][0])\n        else:\n            res.reverse()\n        res\n    proc subtree*(hld: HeavyLightDecomposition, p: int): (int, int) = (hld.rangeL[p], hld.rangeR[p])\n    iterator subtreeV*(hld: HeavyLightDecomposition, p: int):int=\n        for i in hld.rangeL[p]..<hld.rangeR[p]:\n            yield hld.toVtx(i)\n    proc median*(hld: HeavyLightDecomposition, x: int, y: int, z: int): int =\n        hld.lca(x, y) xor hld.lca(y, z) xor hld.lca(x, z)\n    proc la*(hld: HeavyLightDecomposition, starting: int, goal: int, d: int): int =\n        var (u, v, d) = (starting, goal, d)\n        if d < 0:\n            return -1\n        var g = hld.lca(u, v)\n        var dist0 = hld.D[u] - hld.D[g] * 2 + hld.D[v]\n        if dist0 < d:\n            return -1\n        var p = u\n        if hld.D[u] - hld.D[g] < d:\n            p = v\n            d = dist0 - d\n        while hld.D[p] - hld.D[hld.PP[p]] < d:\n            d -= hld.D[p] - hld.D[hld.PP[p]] + 1\n            p = hld.P[hld.PP[p]]\n        hld.I[hld.rangeL[p] - d]\n    iterator children*(hld: HeavyLightDecomposition, v: int): int =\n        var s = hld.rangeL[v] + 1\n        while s < hld.rangeR[v]:\n            var w = hld.toVtx(s)\n            yield w\n            s += hld.rangeR[w] - hld.rangeL[w]\n    \n\n    proc initAuxiliaryTree*(hld:HeavyLightDecomposition,v:seq[int]):UnWeightedUnDirectedTableGraph[int]=\n        var v = v.sortedByit(hld.toseq(it))\n        for i in 0..<(len(v)-1):\n            v.add(hld.lca(v[i],v[i+1]))\n        v = v.sortedByIt(hld.toseq(it)).deduplicate(true)\n        var stack :seq[int]\n        result = initUnWeightedUnDirectedTableGraph[int](v)\n        stack.add(v[0])\n        \n        for i in 1..<len(v):\n            while len(stack) > 0 and hld.toSeq2Out(stack[^1]) < hld.toseq2In(v[i]):\n                discard stack.pop()\n            if len(stack) != 0:\n                result.add_edge(stack[^1],v[i])\n            stack.add(v[i])\n    \n    proc initAuxiliaryWeightedTree*(hld:HeavyLightDecomposition,v:seq[int]):WeightedUnDirectedTableGraph[int,int]=\n        var v = v.sortedByit(hld.toseq(it))\n        for i in 0..<(len(v)-1):\n            v.add(hld.lca(v[i],v[i+1]))\n        v = v.sortedByIt(hld.toseq(it)).deduplicate(true)\n        var stack :seq[int]\n        result = initWeightedUnDirectedTableGraph(v,int)\n        stack.add(v[0])\n        for i in 1..<len(v):\n            while len(stack) > 0 and hld.toSeq2Out(stack[^1]) < hld.toseq2In(v[i]):\n                discard stack.pop()\n            if len(stack) != 0:\n                result.add_edge(stack[^1],v[i],hld.depth(v[i])-hld.depth(stack[^1]))\n            stack.add(v[i])\n\n"


type mint = modint998244353

# 根付き木が与えられる。
# 以下を満たすようなAの個数 mod998

# N 頂点それぞれに1つずつ非負整数を書き込んでいく。

# 部分木のmexはA_iである。

# コレを満たすような書き方が存在するようなAならok



# 自明なこと

# mexはうまくやったとしても部分木サイズくらいまでしか行かない。

# iの子をjとしたときに、必ずA[i] >= A[j]が成立する

# mexより大きかったような頂点数とかが欲しくなるわけでありますね？

# DP[i][mexに関与しなかったような頂点数] = mod998

# 2乗の木DP

var N = ii()
var P = lii(N)

var G = initUnWeightedUnDirectedGraph(N)

for i in 0..<(N-1):
    G.add_edge(P[i]-1,i+1)

var T = initHld(G,0)

var DP = newseq[seq[mint]](N)


proc dfs(x:int)=
    var now = newseqwith(1,mint(1))
    for y in T.children(x):
        dfs(y)
        var (l,r) = T.subtree(y)
        var sz = r-l
        var nxt = newseqwith(len(DP[y])+len(now)-1,mint(0))
        for i in 0..<len(DP[y]):
            for j in 0..<len(now):
                nxt[i+j] += DP[y][i] * now[j]
        now = nxt

    # mexを大きくする方向には好きなだけ増やすことができる

    now = @[mint(0)] & now
    
    for i in range(len(now)-2,-1,-1):
        now[i] += now[i+1]
    
    DP[x] = now

dfs(0)
# echo DP

echo DP[0].sum()