import macros;macro ImportExpand(s:untyped):untyped = parseStmt($s[2])
# {.checks: off.}
ImportExpand "cplib/tmpl/citrus.nim" <=== "when not declared CPLIB_TMPL_CITRUS:\n    const CPLIB_TMPL_CITRUS* = 1\n    {.warning[UnusedImport]: off.}\n    {.hint[XDeclaredButNotUsed]: off.}\n    import os\n    import algorithm\n    import sequtils\n    import tables\n    import macros\n    import std/math\n    import sets\n    import strutils\n    import strformat\n    import sugar\n    import streams\n    import deques\n    import bitops\n    import heapqueue\n    import options\n    import hashes\n    const MODINT998244353* = 998244353\n    const MODINT1000000007* = 1000000007\n    #[ include cplib/utils/infl ]#\n    when not declared CPLIB_UTILS_INFL:\n        const CPLIB_UTILS_INFL* = 1\n        const INFi32* = 100100111.int32\n        const INFL* = int(3300300300300300491)\n    type double* = float64\n    let readNext = iterator(getsChar: bool = false): string {.closure.} =\n        while true:\n            var si: string\n            try: si = stdin.readLine\n            except EOFError: yield \"\"\n            for s in si.split:\n                if getsChar:\n                    for i in 0..<s.len():\n                        yield s[i..i]\n                else:\n                    if s.isEmptyOrWhitespace: continue\n                    yield s\n    proc input*(t: typedesc[string]): string = readNext()\n    proc input*(t: typedesc[char]): char = readNext(true)[0]\n    proc input*(t: typedesc[int]): int = readNext().parseInt\n    proc input*(t: typedesc[float]): float = readNext().parseFloat\n    macro input*(t: typedesc, n: varargs[int]): untyped =\n        var repStr = \"\"\n        for arg in n:\n            repStr &= &\"({arg.repr}).newSeqWith \"\n        parseExpr(&\"{repStr}input({t})\")\n    macro input*(ts: varargs[auto]): untyped =\n        var tupStr = \"\"\n        for t in ts:\n            tupStr &= &\"input({t.repr}),\"\n        parseExpr(&\"({tupStr})\")\n    macro input*(n: int, ts: varargs[auto]): untyped =\n        for typ in ts:\n            if typ.typeKind != ntyAnything:\n                error(\"Expected typedesc, got \" & typ.repr, typ)\n        parseExpr(&\"({n.repr}).newSeqWith input({ts.repr})\")\n    proc `fmtprint`*(x: int or string or char or bool): string = return $x\n    proc `fmtprint`*(x: float or float32 or float64): string = return &\"{x:.16f}\"\n    proc `fmtprint`*[T](x: seq[T] or Deque[T] or HashSet[T] or set[T]): string = return x.toSeq.join(\" \")\n    proc `fmtprint`*[T, N](x: array[T, N]): string = return x.toSeq.join(\" \")\n    proc `fmtprint`*[T](x: HeapQueue[T]): string =\n        var q = x\n        while q.len != 0:\n            result &= &\"{q.pop()}\"\n            if q.len != 0: result &= \" \"\n    proc `fmtprint`*[T](x: CountTable[T]): string =\n        result = x.pairs.toSeq.mapIt(&\"{it[0]}: {it[1]}\").join(\" \")\n    proc `fmtprint`*[K, V](x: Table[K, V]): string =\n        result = x.pairs.toSeq.mapIt(&\"{it[0]}: {it[1]}\").join(\" \")\n    proc print*(prop: tuple[f: File, sepc: string, endc: string, flush: bool], args: varargs[string, `fmtprint`]) =\n        for i in 0..<len(args):\n            prop.f.write(&\"{args[i]}\")\n            if i != len(args) - 1: prop.f.write(prop.sepc) else: prop.f.write(prop.endc)\n        if prop.flush: prop.f.flushFile()\n    proc print*(args: varargs[string, `fmtprint`]) = print((f: stdout, sepc: \" \", endc: \"\\n\", flush: false), args)\n    const LOCAL_DEBUG{.booldefine.} = false\n    macro getSymbolName(x: typed): string = x.toStrLit\n    macro debug*(args: varargs[untyped]): untyped =\n        when LOCAL_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    proc `%`*(x: SomeInteger, y: SomeInteger): 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: SomeInteger, y: SomeInteger): int =\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: SomeInteger, y: SomeInteger): int = x xor y\n    proc `&`*(x: SomeInteger, y: SomeInteger): int = x and y\n    proc `|`*(x: SomeInteger, y: SomeInteger): int = x or y\n    proc `>>`*(x: SomeInteger, y: SomeInteger): int = x shr y\n    proc `<<`*(x: SomeInteger, y: SomeInteger): int = x shl y\n    proc `%=`*(x: var SomeInteger, y: SomeInteger): void = x = x % y\n    proc `//=`*(x: var SomeInteger, y: SomeInteger): void = x = x // y\n    proc `^=`*(x: var SomeInteger, y: SomeInteger): void = x = x ^ y\n    proc `&=`*(x: var SomeInteger, y: SomeInteger): void = x = x & y\n    proc `|=`*(x: var SomeInteger, y: SomeInteger): void = x = x | y\n    proc `>>=`*(x: var SomeInteger, y: SomeInteger): void = x = x >> y\n    proc `<<=`*(x: var SomeInteger, y: SomeInteger): void = x = x << y\n    proc `[]`*(x, n: int): bool = (x and (1 shl n)) != 0\n    proc `[]=`*(x: var int, n: int, i: bool) =\n        if i: x = x or (1 << n)\n        else: (if x[n]: x = x xor (1 << n))\n    proc pow*(a, n: int, m = INFL): int =\n        var\n            rev = 1\n            a = a\n            n = n\n        while n > 0:\n            if n % 2 != 0: rev = (rev * a) mod m\n            if n > 1: a = (a * a) mod m\n            n >>= 1\n        return rev\n    #[ include cplib/math/isqrt ]#\n    when not declared CPLIB_MATH_ISQRT:\n        const CPLIB_MATH_ISQRT* = 1\n        proc isqrt*(n: int): int =\n            var x = n\n            var y = (x + 1) shr 1\n            while y < x:\n                x = y\n                y = (x + n div x) shr 1\n            return x\n    proc chmax*[T](x: var T, y: T): bool {.discardable.} = (if x < y: (x = y; return true; ) return false)\n    proc chmin*[T](x: var T, y: T): bool {.discardable.} = (if x > y: (x = y; return true; ) return false)\n    proc `max=`*[T](x: var T, y: T) = x = max(x, y)\n    proc `min=`*[T](x: var T, y: T) = x = min(x, y)\n    proc at*(x: char, a = '0'): int = int(x) - int(a)\n    proc Yes*(b: bool = true): void = print(if b: \"Yes\" else: \"No\")\n    proc No*(b: bool = true): void = Yes(not b)\n    proc YES_upper*(b: bool = true): void = print(if b: \"YES\" else: \"NO\")\n    proc NO_upper*(b: bool = true): void = Yes_upper(not b)\n    const DXY* = [(0, -1), (0, 1), (-1, 0), (1, 0)]\n    const DDXY* = [(1, -1), (1, 0), (1, 1), (0, -1), (0, 1), (-1, -1), (-1, 0), (-1, 1)]\n    macro exit*(statement: untyped): untyped = (quote do: (`statement`; quit()))\n    proc initHashSet[T](): Hashset[T] = initHashSet[T](0)\n"
ImportExpand "cplib/modint/modint.nim" <=== "when not declared CPLIB_MODINT_MODINT:\n    const CPLIB_MODINT_MODINT* = 1\n    #[ include cplib/modint/barrett_impl ]#\n    when not declared CPLIB_MODINT_MODINT_BARRETT:\n        const CPLIB_MODINT_MODINT_BARRETT* = 1\n        import std/macros\n        type StaticBarrettModint*[M: static[uint32]] = object\n            a: uint32\n        type DynamicBarrettModint*[M: static[uint32]] = object\n            a: uint32\n        type BarrettModint* = StaticBarrettModint or DynamicBarrettModint\n    \n        proc get_im*(M: uint32): uint = cast[uint](-1) div M + 1\n        func get_param*[M: static[uint32]](self: typedesc[DynamicBarrettModint[M]]): ptr[tuple[M, im: uint]] =\n            {.cast(noSideEffect).}:\n                var p {.global.}: tuple[M, im: uint] = (998244353u, get_im(998244353u32))\n                return p.addr\n        template get_M*(T: typedesc[BarrettModint]): uint =\n            when T is StaticBarrettModint: T.M.uint\n            else: (get_param(T))[].M.uint\n        proc setMod*[T: static[uint32]](self: typedesc[DynamicBarrettModint[T]], M: SomeInteger or SomeUnsignedInt) =\n            (get_param(self))[] = (M: M.uint, im: get_im(M.uint32))\n    \n        template umod*[T: BarrettModint](self: typedesc[T] or T): uint32 =\n            when self is typedesc:\n                when self is StaticBarrettModint: self.M\n                else: cast[uint32](((get_param(self))[]).M)\n            else: T.umod\n        template `mod`*[T: BarrettModint](self: typedesc[T] or T): int32 = (T.umod).int32\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)(((__uint128_t)(a) * b) >> 64);\n        }\n        \"\"\".}\n        proc calc_mul*(a, b: culonglong): culonglong {.importcpp: \"calc_mul(#, #)\", nodecl, inline.}\n        proc rem*(T: typedesc[BarrettModint], a: uint): uint32 =\n            when T is StaticBarrettModint:\n                const im = get_im(T.M)\n                const M = get_M(T)\n                var x = (calc_mul(cast[culonglong](a), cast[culonglong](im))).uint\n                var r = a - x * M\n                if M <= r: r += M\n                return cast[uint32](r)\n            else:\n                var p = get_param(T)[]\n                var x = (calc_mul(cast[culonglong](a), cast[culonglong](p.im))).uint\n                var r = a - x * p.M\n                if p.M <= r: r += p.M\n                return cast[uint32](r)\n        proc init*(T: typedesc[BarrettModint], a: T or SomeInteger): auto =\n            when a is T: return a\n            else:\n                if a in 0..<T.mod.int: return T(a: a.uint32)\n                var a = a mod T.mod.int\n                if a < 0: a += T.mod.int\n                return T(a: a.uint32)\n    \n        proc `-`*[T: BarrettModint](a: T): T = T(a: T.umod - a.a)\n        proc `+=`*[T: BarrettModint](a: var T, b: T or SomeInteger) =\n            a.a += init(T, b).a\n            if a.a >= T.umod: a.a -= T.umod\n        proc `-=`*[T: BarrettModint](a: var T, b: T or SomeInteger) =\n            a.a -= init(T, b).a\n            if a.a >= T.umod: a.a += T.umod\n        proc `*=`*[T: BarrettModint] (a: var T, b: T or SomeInteger) =\n            a.a = rem(T, (a.a).uint * (init(T, b).a).uint)\n        proc inv*[T: BarrettModint](x: T): T =\n            var x: int32 = int32(x.val)\n            var y: int32 = T.mod\n            var u = 1i32\n            var v, t = 0i32\n            while y > 0:\n                t = x div y\n                x -= t * y\n                u -= t * v\n                swap(x, y)\n                swap(u, v)\n            return init(T, u)\n        proc `/=`*[T: BarrettModint](a: var T, b: T or SomeInteger) = a *= init(T, b).inv\n        proc val*(a: BarrettModint): int = a.a.int\n        macro declarStaticBarrettModint*(name, M) =\n            let converter_name = ident(\"to\" & $`name`)\n            quote do:\n                type `name`* = StaticBarrettModint[`M`]\n                converter `converter_name`*(a: int): StaticBarrettModint[`M`] = init(StaticBarrettModint[`M`], a)\n        macro declarDynamicBarrettModint*(name, id) =\n            let converter_name = ident(\"to\" & $`name`)\n            quote do:\n                type `name`* = DynamicBarrettModint[`id`]\n                converter `converter_name`*(a: int): DynamicBarrettModint[`id`] = init(DynamicBarrettModint[`id`], a)\n    #[ include cplib/modint/montgomery_impl ]#\n    when not declared CPLIB_MODINT_MODINT_MONTGOMERY:\n        const CPLIB_MODINT_MODINT_MONTGOMERY* = 1\n        import std/macros\n        type StaticMontgomeryModint*[M: static[uint32]] = object\n            a: uint32\n        type DynamicMontgomeryModint*[M: static[uint32]] = object\n            a: uint32\n        type MontgomeryModint* = StaticMontgomeryModint or DynamicMontgomeryModint\n    \n        proc get_r*(M: uint32): uint32 =\n            result = M\n            for _ in 0..<4: result *= 2u32 - M * result\n        proc get_n2*(M: uint32): uint32 = uint32((not uint(M - 1u32)) mod uint(M))\n        proc check_params(M, r: uint32) =\n            assert M < (1u32 shl 30), \"invalid mod >= 2^30\"\n            assert (M and 1u32) == 1u32, \"invalid mod % 2 == 0\"\n            assert r * M == 1, \"r * mod != 1\"\n        func get_param*[M: static[uint32]](self: typedesc[DynamicMontgomeryModint[M]]): ptr[tuple[M, r, n2: uint32]] =\n            {.cast(noSideEffect).}:\n                var p {.global.}: tuple[M, r, n2: uint32] = (998244353u32, get_r(998244353u32), get_n2(998244353u32))\n                return p.addr\n        template get_M*(T: typedesc[MontgomeryModint]): uint32 =\n            when T is StaticMontgomeryModint: T.M\n            else: (get_param(T))[].M\n        proc setMod*[T: static[uint32]](self: typedesc[DynamicMontgomeryModint[T]], M: SomeInteger or SomeUnsignedInt) =\n            var r = get_r(M.uint32)\n            var n2 = get_n2(M.uint32)\n            var p = (M.uint32, r, n2)\n            (get_param(self))[] = p\n            check_params(M.uint32, r)\n    \n        template umod*[T: MontgomeryModint](self: typedesc[T] or T): uint32 =\n            when self is typedesc:\n                when self is StaticMontgomeryModint: self.M\n                else: ((get_param(self))[]).M\n            else: T.umod\n        template `mod`*[T: MontgomeryModint](self: typedesc[T] or T): int32 = (T.umod).int32\n    \n        func reduce(T: typedesc[MontgomeryModint], b: uint): uint32 =\n            when T is StaticMontgomeryModint:\n                const r = get_r(T.M)\n                return cast[uint32]((b + uint(cast[uint32](b) * (not (r - 1u32))) * T.M) shr 32)\n            else:\n                var p = (get_param(T))[]\n                return cast[uint32]((b + uint(cast[uint32](b) * (not (p.r - 1u32))) * p.M) shr 32)\n        proc init*(T: typedesc[MontgomeryModint], a: T or SomeInteger): auto =\n            when a is T: return a\n            elif T is StaticMontgomeryModint:\n                const r = get_r(T.M)\n                const n2 = get_n2(T.M)\n                check_params(T.M, r)\n                var ai = reduce(T, uint(a.int32 mod T.M.int32 + T.M.int32) * n2)\n                result = StaticMontgomeryModint[T.M](a: ai)\n            elif T is DynamicMontgomeryModint:\n                var p = (get_param(T))[]\n                var ai = reduce(T, uint(a.int32 mod p.M.int32 + p.M.int32) * p.n2)\n                result = DynamicMontgomeryModint[T.M](a: ai)\n    \n        proc `+=`*[T: MontgomeryModint](a: var T, b: T or SomeInteger) =\n            a.a += init(T, b).a - T.get_M * 2u32\n            if cast[int32](a.a) < 0i32: a.a += T.get_M * 2u32\n        proc `-=`*[T: MontgomeryModint](a: var T, b: T or SomeInteger) =\n            a.a -= init(T, b).a\n            if cast[int32](a.a) < 0i32: a.a += T.get_M * 2u32\n        proc val*[T: MontgomeryModint](a: T): int =\n            result = reduce(T, a.a).int\n            if result.uint32 >= T.get_M: result -= T.get_M.int\n    \n        proc `-`*[T: MontgomeryModint](a: T): T = init(T, 0) - a\n        proc `*=`*[T: MontgomeryModint] (a: var T, b: T or SomeInteger) = a.a = reduce(T, uint(a.a) * init(T, b).a)\n        proc inv*[T: MontgomeryModint](x: T): T =\n            var x: int32 = int32(x.val)\n            var y: int32 = T.mod\n            var u = 1i32\n            var v, t = 0i32\n            while y > 0:\n                t = x div y\n                x -= t * y\n                u -= t * v\n                swap(x, y)\n                swap(u, v)\n            return init(T, u)\n        proc `/=`*[T: MontgomeryModint](a: var T, b: T or SomeInteger) = a *= init(T, b).inv\n    \n        macro declarStaticMontgomeryModint*(name, M) =\n            let converter_name = ident(\"to\" & $`name`)\n            quote do:\n                type `name`* = StaticMontgomeryModint[`M`]\n                converter `converter_name`*(a: int): StaticMontgomeryModint[`M`] = init(StaticMontgomeryModint[`M`], a)\n        macro declarDynamicMontgomeryModint*(name, id) =\n            let converter_name = ident(\"to\" & $`name`)\n            quote do:\n                type `name`* = DynamicMontgomeryModint[`id`]\n                converter `converter_name`*(a: int): DynamicMontgomeryModint[`id`] = init(DynamicMontgomeryModint[`id`], a)\n    \n        declarDynamicMontgomeryModint(modint_montgomery, 1u32)\n    import std/math\n    import std/algorithm\n    #[ import cplib/math/isqrt ]#\n    declarStaticMontgomeryModint(mint998244353_montgomery, 998244353u32)\n    declarStaticMontgomeryModint(mint1000000007_montgomery, 1000000007u32)\n    declarDynamicMontgomeryModint(mint_montgomery, 1u32)\n    declarStaticBarrettModint(mint998244353_barrett, 998244353u32)\n    declarStaticBarrettModint(mint1000000007_barrett, 1000000007u32)\n    declarDynamicBarrettModint(mint_barrett, 1u32)\n    func `+`*(a, b: MontgomeryModint or BarrettModint): auto = (result = a; result += b)\n    func `-`*(a, b: MontgomeryModint or BarrettModint): auto = (result = a; result -= b)\n    func `*`*(a, b: MontgomeryModint or BarrettModint): auto = (result = a; result *= b)\n    func `/`*(a, b: MontgomeryModint or BarrettModint): auto = (result = a; result /= b)\n    func `+`*(a: MontgomeryModint or BarrettModint, b: SomeInteger): auto = (result = a; result += b)\n    func `-`*(a: MontgomeryModint or BarrettModint, b: SomeInteger): auto = (result = a; result -= b)\n    func `*`*(a: MontgomeryModint or BarrettModint, b: SomeInteger): auto = (result = a; result *= b)\n    func `/`*(a: MontgomeryModint or BarrettModint, b: SomeInteger): auto = (result = a; result /= b)\n    func `+`*(a: SomeInteger, b: MontgomeryModint or BarrettModint): auto = b + a\n    func `-`*(a: SomeInteger, b: MontgomeryModint or BarrettModint): auto = b - a\n    func `*`*(a: SomeInteger, b: MontgomeryModint or BarrettModint): auto = b * a\n    func `/`*(a: SomeInteger, b: MontgomeryModint or BarrettModint): auto = b / a\n    func pow*(a: MontgomeryModint or BarrettModint, n: int): auto =\n        result = init(typeof(a), 1)\n        var a = a\n        var n = n\n        while n > 0:\n            if (n and 1) == 1: result *= a\n            a *= a\n            n = (n shr 1)\n    func `$`*(a: MontgomeryModint or BarrettModint): string = $(a.val)\n    proc estimate_rational*(a: MontgomeryModint or BarrettModint, ub: int = isqrt(typeof(a).mod)): string =\n        var v: seq[tuple[s, n, d: int]]\n        for d in 1..ub:\n            var n = (a * d).val\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        return $v[0].n & \"/\" & $v[0].d\n"
ImportExpand "cplib/graph/graph.nim" <=== "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"
type mint = mint998244353_barrett

var n, m, k = input(int)
var g = initUnWeightedUnDirectedStaticGraph(n)
for i in 0..<m:
    var u, v = input(int)-1
    g.add_edge(u, v)
g.build

proc itoparam(x: int): (int, seq[int]) =
    var x = x
    var a = newSeq[int](n)
    for i in 0..<n:
        a[i] = x % (k+1)
        x //= (k+1)
    return (x, a)
proc paramtoi(x: int, a: seq[int]): int =
    result = x
    for ai in a.reversed:
        result = result * (k+1) + ai

var dp = newSeqWith(n*pow(k+1, n), mint(0))
for i in 0..<n:
    var a = newseqwith(n, k)
    a[i] = k-1
    dp[paramtoi(i, a)] = mint(1)

for i in 0..<(n*k)-1:
    var dpn = newseqwith(dp.len, mint(0))
    for j in 0..<dp.len:
        if dp[j].val == 0: continue
        var (u, a) = itoparam(j)
        for v in g[u]:
            if a[v] == 0: continue
            var a = a
            a[v] -= 1
            dpn[paramtoi(v, a)] += dp[j]
    swap(dp, dpn)

var ans = mint(0)
for i in 0..<n:
    ans += dp[paramtoi(i, newseqwith(n, 0))]
print(ans.val)