static void Main()
{
var n = int.Parse(Console.ReadLine());
var edges = Enumerable.Repeat(0, n - 1).Select(_ => Console.ReadLine().Split().Select(x => int.Parse(x) - 1).ToArray()).ToArray();
int k = int.Parse(Console.ReadLine());
Node[] nodes = new Node[n];
for (int i = 0; i < k; i++)
{
var vp = Console.ReadLine().Split().Select(int.Parse).ToArray();
nodes[vp[0] - 1] = new Node(vp[1] % 2 == 0 ? Parity.Even : Parity.Odd, vp[1], vp[1]);
}
var IdentityElement = new Node(Parity.Both, int.MinValue / 2, int.MaxValue / 2);
ReRooting <Node> rerooting = new ReRooting <Node>(n, edges, IdentityElement, Node.Merge, Node.Next, (x, index) => Node.Merge(x, nodes[index] ?? IdentityElement));
var res = new Node[n];
for (int i = 0; i < n; i++)
{
var query = rerooting.Query(i);
if (query.Parity == Parity.None || query.LowerBound > query.UpperBound || (query.LowerBound == query.UpperBound && ((query.Parity == Parity.Even) ^ query.LowerBound % 2 == 0)))
{
goto invalid;
}
res[i] = query;
}
Console.WriteLine("Yes");
Console.WriteLine(string.Join("\n", res.Select(x => x.UpperBound)));
return;
invalid :;
Console.WriteLine("No");
}
public static void Main()
{
var n = int.Parse(Console.ReadLine());
var edges = Enumerable.Repeat(0, n - 1).Select(_ => Console.ReadLine().Split().Select(x => int.Parse(x) - 1).ToArray()).ToArray();
ReRooting <Data> res =
new ReRooting <Data>(
n,
edges,
new Data()
{
Combination = 1, Count = 0
},
(x, y) =>
{
var newCount = x.Count + y.Count;
return(new Data()
{
Combination = x.Combination * y.Combination * Factorial(newCount) / Factorial(x.Count) / Factorial(y.Count),
Count = newCount
});
},
(x, _) => new Data()
{
Combination = x.Combination,
Count = x.Count + 1
});
for (int i = 0; i < n; i++)
{
Console.WriteLine(res.Query(i).Combination);
}
}
public static void Main()
{
var nk = Console.ReadLine().Split().Select(int.Parse).ToArray();
var n = nk[0];
var k = nk[1];
ReRooting <Tuple <long, int[]> > hoge = new ReRooting <Tuple <long, int[]> >(
n,
Enumerable.Repeat(0, n - 1).Select(_ => Console.ReadLine().Split().Select(x => int.Parse(x) - 1).ToArray()).ToArray(),
new Tuple <long, int[]>(0, new int[k]),
(x, y) =>
{
return(new Tuple <long, int[]>(x.Item1 + y.Item1,
(x.Item2.Zip(y.Item2, (X, Y) => X + Y).ToArray())
));
},
(x, y) =>
{
var res = new int[k];
for (int i = 0; i < k - 1; i++)
{
res[i + 1] = x.Item2[i];
}
res[0] = x.Item2[k - 1] + 1;
return(new Tuple <long, int[]>(x.Item1 + res[0], res));
}
);
Console.WriteLine((Enumerable.Range(0, n).Sum(x => hoge.Query(x).Item1 - hoge.Query(x).Item2[0])) / 2);
}
public static void Main()
{
var n = int.Parse(Console.ReadLine());
ReRooting <Data> rerooting = new ReRooting <Data>(
n,
Enumerable.Repeat(0, n - 1).Select(_ => Console.ReadLine().Split().Select(x => int.Parse(x) - 1).ToArray()).ToArray(),
new Data()
{
Available = 0, Unavailable = 0
},
Data.Merge,
(node, _) => node,
(node, _) => Data.AddEdge(node)
);
int res = 0;
for (int i = 0; i < n; i++)
{
var query = rerooting.Query(i);
if (query.Available == query.Unavailable)
{
res++;
}
}
Console.WriteLine(res);
}
public static void Main()
{
int n = int.Parse(Console.ReadLine());
var edges = new int[n - 1][];
List <int>[] tree = Enumerable.Repeat(0, n).Select(_ => new List <int>()).ToArray();
for (int i = 0; i < n - 1; i++)
{
var st = Console.ReadLine().Split().Select(x => int.Parse(x) - 1).ToArray();
edges[i] = st;
tree[st[0]].Add(st[1]);
tree[st[1]].Add(st[0]);
}
ReRooting <int> subTreeSizes = new ReRooting <int>(n, edges, 0, (x, y) => x + y, x => x + 1);
ModInt prob = 0;
for (int i = 0; i < n; i++)
{
//白の時、他の部分木の2つ以上に着色があればいい
//一つ、ゼロの余事象
ModInt zeroProb = 1 / Power(2, n - 1);
ModInt oneProb = 0;
foreach (var subtreeSize in subTreeSizes.dp[i])
{
var any = 1 - 1 / Power(2, subtreeSize);
oneProb += 1 / Power(2, n - subtreeSize - 1) * any;
}
prob += 1 - zeroProb - oneProb;
}
Console.WriteLine(prob / 2);
}
static void Main()
{
var n = int.Parse(Console.ReadLine());
var edges = Enumerable.Repeat(0, n - 1).Select(_ => Console.ReadLine().Split().Select(x => int.Parse(x) - 1).ToArray()).ToArray();
ReRooting <int> getDiameter = new ReRooting <int>(n, edges, 0, Max, x => x + 1);
var diameter = Enumerable.Range(0, n).Select(x => getDiameter.Query(x)).Max() - 1;
Console.WriteLine(diameter % 3 == 1 ? "Second" : "First");
}
static void Main()
{
int n = int.Parse(Console.ReadLine());
List <int>[] neighbours = Enumerable.Repeat(0, n).Select(_ => new List <int>()).ToArray();
int[][] edges = Enumerable.Repeat(0, n - 1).Select(_ => Console.ReadLine().Split().Select(x => int.Parse(x) - 1).ToArray()).ToArray();
ReRooting treeDP = new ReRooting(n, edges);
Console.WriteLine(string.Join("\n", Enumerable.Range(0, n).Select(x => treeDP.Query(x))));
}
static void Main()
{
var nm = Console.ReadLine().Split().Select(int.Parse).ToArray();
var n = nm[0];
Mod = nm[1];
List <int>[] neighbours = Enumerable.Repeat(0, n).Select(_ => new List <int>()).ToArray();
int[][] edges = Enumerable.Repeat(0, n - 1).Select(_ => Console.ReadLine().Split().Select(x => int.Parse(x) - 1).ToArray()).ToArray();
ReRooting <long> treeDP = new ReRooting <long>(n, edges, 1, (x, y) => (x * y) % nm[1], x => x + 1);
Console.WriteLine(string.Join("\n", Enumerable.Range(0, n).Select(x => treeDP.Query(x) - 1)));
}
public static void Main()
{
int n = int.Parse(Console.ReadLine());
List <int[]> edges = new List <int[]>();
for (int i = 1; i < n; i++)
{
edges.Add(new int[] { i, int.Parse(Console.ReadLine()) });
}
var reRooting = new ReRooting <int>(n, edges.ToArray(), 0, (x, y) => x + y, (x, _) => x + 1);
for (int i = 0; i < reRooting.NodeCount; i++)
{
Console.WriteLine(reRooting.DP[i].Max());
}
}
public static void Main()
{
int n = NextInt;
int[][] edges = new int[n - 1][];
for (int i = 1; i < n; i++)
{
edges[i - 1] = new int[] { i, NextInt };
}
ReRooting <int> rerooting = new ReRooting <int>(n, edges, 0, (x, y) => x + y, (x, _) => x + 1);
for (int i = 0; i < n; i++)
{
Console.WriteLine(rerooting.DP[i].Max());
}
}
static void Main()
{
int n = int.Parse(Console.ReadLine());
List <int>[] neighbours = Enumerable.Repeat(0, n).Select(_ => new List <int>()).ToArray();
int[][] edges = Enumerable.Repeat(0, n - 1).Select(_ => Console.ReadLine().Split().Select(x => int.Parse(x) - 1).ToArray()).ToArray();
ReRooting treeDP = new ReRooting(n, edges);
var dicts = treeDP.Neighbours.Select(x => x.Select((y, z) => new Tuple <int, int>(y, z)).ToDictionary(y => y.Item1, y => y.Item2)).ToArray();
var sums = Console.ReadLine().Split().Select(long.Parse).ToArray();
int eqIndex = -1;
long[] res = new long[edges.Length];
BigInteger sum = new BigInteger(0);
for (int i = 0; i < sums.Length; i++)
{
sum += sums[i];
}
for (int i = 0; i < edges.Length; i++)
{
var edge = edges[i];
long atob = treeDP.Query(edge[0], dicts[edge[0]][edge[1]]);
long btoa = treeDP.Query(edge[1], dicts[edge[1]][edge[0]]);
if (atob == btoa)
{
res[i] = 0;
eqIndex = i;
}
else
{
res[i] = (Abs(Abs(sums[edge[0]] - sums[edge[1]]) / (Abs(atob - btoa))));
sum -= (2 * res[i] * new BigInteger(atob) * btoa);
}
}
if (eqIndex >= 0)
{
BigInteger zeroatob = treeDP.Query(edges[eqIndex][0], dicts[edges[eqIndex][0]][edges[eqIndex][1]]);
BigInteger zerobtoa = treeDP.Query(edges[eqIndex][1], dicts[edges[eqIndex][1]][edges[eqIndex][0]]);
res[eqIndex] = (long)(sum / (zeroatob * zerobtoa * 2));
}
Console.WriteLine(string.Join("\n", res));
}
static void Solve()
{
var nabd = Console.ReadLine().Split().Select(int.Parse).ToArray();
var n = nabd[0];
var a = nabd[1] - 1;
var b = nabd[2] - 1;
var da = nabd[3];
var db = nabd[4];
var edges = Enumerable.Repeat(0, n - 1).Select(_ => Console.ReadLine().Split().Select(x => int.Parse(x) - 1).ToArray()).ToArray();
ReRooting <int> rerooting = new ReRooting <int>(n, edges, 0, Max, (x, _) => x + 1);
int[] distance = Enumerable.Repeat(-1, n).ToArray();
Stack <int> stack = new Stack <int>();
stack.Push(a);
distance[a] = 0;
while (stack.Count != 0)
{
var parent = stack.Pop();
foreach (var adj in rerooting.Adjacents[parent])
{
if (distance[adj] != -1)
{
continue;
}
distance[adj] = distance[parent] + 1;
stack.Push(adj);
}
}
var d = Enumerable.Range(0, n).Select(rerooting.Query).Max() - 1;
if (db <= da * 2 || d <= da * 2 || distance[b] <= da)
{
Console.WriteLine("Alice");
}
else
{
Console.WriteLine("Bob");
}
}
public static void Main()
{
int n = int.Parse(Console.ReadLine());
var edges = Enumerable.Repeat(0, n - 1).Select(_ => Console.ReadLine().Split().Select(x => int.Parse(x) - 1).ToArray()).ToArray();
List <int>[] graph = Enumerable.Repeat(0, n).Select(_ => new List <int>()).ToArray();
for (int i = 0; i < n - 1; i++)
{
var st = edges[0];
graph[st[0]].Add(st[1]);
graph[st[1]].Add(st[0]);
}
long[] sums = new long[n];
Dictionary <int, long>[] dics = Enumerable.Repeat(0, n).Select(_ => new Dictionary <int, long>()).ToArray();
int q = int.Parse(Console.ReadLine());
for (int i = 0; i < q; i++)
{
var tex = Console.ReadLine().Split().Select(int.Parse).ToArray();
var ind = tex[1] - 1;
var(node, par) = tex[0] == 1 ? (edges[ind][0], edges[ind][1]) : (edges[ind][1], edges[ind][0]);
var x = tex[2];
if (!dics[node].ContainsKey(par))
{
dics[node][par] = 0;
}
sums[node] += x;
dics[node][par] += x;
}
ReRooting <long> rerooting = new ReRooting <long>(n, edges, 0, (x, y) => x + y, (val, node, par) => val + sums[node] - (dics[node].ContainsKey(par) ? dics[node][par] : 0));
for (int i = 0; i < n; i++)
{
Console.WriteLine(rerooting.Query(i));
}
}
public static void Main()
{
int n = int.Parse(Console.ReadLine());
List <int>[] graph = Enumerable.Repeat(0, n).Select(_ => new List <int>()).ToArray();
int[][] edges = new int[n - 1][];
for (int i = 0; i < n - 1; i++)
{
var st = Console.ReadLine().Split().Select(x => int.Parse(x) - 1).ToArray();
edges[i] = st;
graph[st[0]].Add(st[1]);
graph[st[1]].Add(st[0]);
}
ReRooting <int> diamator = new ReRooting <int>(n, edges, 0, Max, (x, _) => x + 1);
var max = Enumerable.Range(0, n).Max(x => diamator.Query(x));
var firstInd = Enumerable.Range(0, n).TakeWhile(x => diamator.Query(x) != max).Count();
Stack <int> stack = new Stack <int>();
stack.Push(firstInd);
int[] distances = new int[n];
while (stack.Count > 0)
{
var elem = stack.Pop();
foreach (var item in graph[elem])
{
if (item == firstInd || distances[item] != 0)
{
continue;
}
distances[item] = distances[elem] + 1;
stack.Push(item);
}
}
var secondInd = distances.TakeWhile(x => x != max - 1).Count();
Console.WriteLine($"{firstInd + 1} {secondInd + 1}");
}
public static void Main()
{
int n = int.Parse(Console.ReadLine());
var edges = Enumerable.Repeat(0, n - 1).Select(_ => Console.ReadLine().Split().Select(x => int.Parse(x) - 1).ToArray()).ToArray();
ReRooting <int> rerooting = new ReRooting <int>(n, edges, 0, Max, (x, _) => x + 1);
var rerootingRes = Enumerable.Range(0, n).Select(rerooting.Query).ToArray();
var max = rerootingRes.Max();
var maxInd = Array.IndexOf(rerootingRes, max);
List <int>[] graph = Enumerable.Repeat(0, n).Select(_ => new List <int>()).ToArray();
foreach (var st in edges)
{
graph[st[0]].Add(st[1]);
graph[st[1]].Add(st[0]);
}
Stack <(ImmutableStack <int>, int)> stack = new Stack <(ImmutableStack <int>, int)>();
stack.Push((new ImmutableStack <int>().Push(maxInd), -1));
var maxSeq = new ImmutableStack <int>();
while (stack.Count != 0)
{
var(seq, prev) = stack.Pop();
if (maxSeq.Count < seq.Count)
{
maxSeq = seq;
}
var node = seq.Top;
foreach (var adj in graph[node])
{
if (adj == prev)
{
continue;
}
stack.Push((seq.Push(adj), node));
}
}
List <int> stem = new List <int>();
while (maxSeq.Count != 0)
{
stem.Add(maxSeq.Top);
maxSeq = maxSeq.Pop();
}
var dic = stem.ToDictionary(x => x, x => 0);
for (int i = 0; i < n; i++)
{
if (dic.ContainsKey(i))
{
continue;
}
var parent = graph[i].First();
if (graph[i].Count != 1 || !dic.ContainsKey(parent))
{
Console.WriteLine(-1);
return;
}
dic[parent]++;
}
for (int i = 0; i < stem.Count; i++)
{
if (dic[stem[i]] < dic[stem[^ (i + 1)]])