import macros;macro ImportExpand(s:untyped):untyped = parseStmt($s[2])
ImportExpand "cplib/tree/heavylightdecomposition.nim" <=== "when not declared CPLIB_TREE_HLD:\n    const CPLIB_TREE_HLD* = 1\n    import sequtils\n    import algorithm\n    import sets\n    #[ import cplib/graph/graph ]#\n    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    # 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    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        ## 根が欲しかったらG.v[0]を使ってください　けむにく\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        ## 根が欲しかったらG.v[0]を使ってください　けむにく\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"
ImportExpand "cplib/graph/graph.nim" <=== ""
import sequtils
type NamoriGraph = ref object 
    tree : HeavyLightDecomposition
    rootNo : seq[int]
    roots : seq[int]
    cyclesize : int


proc initNamoriGraph(graph:UnWeightedUnDirectedGraph):NamoriGraph=
    var stack : seq[int]
    var sizes = newseqwith(len(graph),0)
    var rootNo = newseqwith(len(graph),-1)
    var tree = initUnWeightedUnDirectedGraph(len(graph)+1)
    var roots = newseqwith(len(graph),0)
    for i in 0..<len(graph):
        sizes[i] = len(graph.edges[i])
        if sizes[i] == 1:
            stack.add(i)
    while len(stack) != 0:
        var i = stack.pop()
        for j in graph[i]:
            if sizes[j] != 1:
                tree.add_edge(i,j)
                sizes[j] -= 1
                if sizes[j] == 1:
                    stack.add(j)
    for i in 0..<len(graph):
        if sizes[i] != 1:
            var now = i
            var bef = -1
            var tmp = 1
            rootNo[i] = 0
            while true:
                
                tree.add_edge(now,len(graph))
                var next = -1
                proc dfs(x,p:int)=
                    roots[x] = now
                    for y in graph[x]:
                        if p != y:
                            if sizes[y] == 1:
                                dfs(y,x)
                            elif bef != y:
                                next = y
                dfs(now,-1)
                if next == -1 or next == i:
                    break
                bef = now
                now = next
                rootNo[now] = tmp
                tmp += 1
            #dump_graph(tree)
            return NamoriGraph(tree:tree.initHld(len(graph)),rootNo:rootNo,roots:roots,cyclesize:tmp)

proc dist(namori:NamoriGraph,u,v:int):(int,int)=
    ## u,v間の距離を二通り返します
    ## (小さいほう,大きいほう)
    ## ただし、一通りしか存在しない場合二つ目のintは-1を返します。
    var lca = namori.tree.lca(u,v) 
    if lca != len(namori.rootNo):
        return (namori.tree.dist(u,v),-1)
    else:
        var x = namori.roots[u]
        var y = namori.roots[v]
        var a = abs(namori.rootNo[x]-namori.rootNo[y])
        var b = namori.cyclesize - a
        var tmp = namori.tree.depth(u) + namori.tree.depth(v) - 2
        return (min(a,b)+tmp,max(a,b)+tmp)

proc incycle(namori:NamoriGraph,x:int):bool=
    return namori.rootNo[x] != -1


ImportExpand "cplib/tmpl/sheep.nim" <=== "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':\n                break\n            result &= c\n    #chmin,chmax\n    template `max=`(x, y) = x = max(x, y)\n    template `min=`(x, y) = x = min(x, y)\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    #[ include cplib/utils/constants ]#\n    when not declared CPLIB_UTILS_CONSTANTS:\n        const CPLIB_UTILS_CONSTANTS* = 1\n        const INF32*: int32 = 100100111.int32\n        const INF64*: int = int(3300300300300300491)\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"
var N = ii()
var G = initUnWeightedUnDirectedGraph(N)
var edges : seq[(int,int)]
for i in range(N):
    var a,b = ii()-1
    G.add_edge(a,b)
    edges.add (a,b)
var namori = G.initNamoriGraph()
var ans : seq[int]
for i in range(N):
    var (a,b) = edges[i]
    if namori.incycle(a) and namori.incycle(b):
        ans.add(i+1)

echo len(ans)
echo ans.join(" ")