Building Forest

### 题意翻译 一个有向加权森林是无环有向加权图，其中每个顶点至多有一条边。有向加权森林中，顶点 $ v $ 的根是一个没有出边的顶点，并且可以通过沿着加权有向森林的边从顶点 $ v $ 到达。现将顶点 $ v $ 的根记为 $ root(v) $。顶点v的深度是从顶点 $ v $ 到其根的路径的权重之和。现将顶点 $ v $ 的深度表示为 $ depth(v) $。 构建加权定向森林的过程如下：最初，森林不包含顶点。顶点按顺序逐个添加。总体而言，有 $ n $ 个执行的加法操作。 第 $ i（i>0）$个 操作由一组数字 （$ k $,$ v1 $，$ x1 $，$ v2 $， $ x2 $， ... $ vk $，$ xk $） 描述，意味着我们应该将顶点 $ i $ 下的边 $ k $ 添加到图中。 从顶点 $root( v_1 )$ 到顶点$ i $的边，权重为 $depth( v_1 ) + x_1 $；从顶点 $root( v2 )$ 到顶点$ i $的边，权重为 $ depth( v2 ) +  x2 $ ，以此类推。如果 $ k=0 $，那么图中只增加了顶点 $ i $ ，没有增加任何边。 现给定添加的顶点，请计算森林所有边的权重之和。由于数据可能很大，请将输出的数据模 $1000000007$ $（10^9 + 7）$。 ### 输入格式 第一行包含一个整数 $ n (1 ≤ n ≤ 10^5) $ 接下来的 $ n $ 行表示操作，第 $ i $ 行包含添加第 $ i $ 个顶点的操作说明 每行的第一个数字为整数 $ k (0 ≤ k ≤ i - 1) $之后是 $ 2k $ 空格分隔的整数： $v1, x1, v2, x2, ... , vk, xk. (1 ≤ vj ≤ i - 1, |xj| ≤ 10^9) $。 保证所有操作的总和 $ k $ 不超过 $ 10^5 $ ,同时保证添加顶点的操作不会导致环和重边。 ### 输出格式 一行一个整数表示图中所有边的权重之和，模数为$ 1000000007 (10^9 + 7) $。

An oriented weighted forest is an acyclic weighted digraph in which from each vertex at most one edge goes. The root of vertex $ v $ of an oriented weighted forest is a vertex from which no edge goes and which can be reached from vertex $ v $ moving along the edges of the weighted oriented forest. We denote the root of vertex $ v $ as $ root(v) $ . The depth of vertex $ v $ is the sum of weights of paths passing from the vertex $ v $ to its root. Let's denote the depth of the vertex $ v $ as $ depth(v) $ . Let's consider the process of constructing a weighted directed forest. Initially, the forest does not contain vertices. Vertices are added sequentially one by one. Overall, there are $ n $ performed operations of adding. The $ i $ -th $ (i>0) $ adding operation is described by a set of numbers $ (k,v_{1},x_{1},v_{2},x_{2},...\ ,v_{k},x_{k}) $ and means that we should add vertex number $ i $ and $ k $ edges to the graph: an edge from vertex $ root(v_{1}) $ to vertex $ i $ with weight $ depth(v_{1})+x_{1} $ , an edge from vertex $ root(v_{2}) $ to vertex $ i $ with weight $ depth(v_{2})+x_{2} $ and so on. If $ k=0 $ , then only vertex $ i $ is added to the graph, there are no added edges. Your task is like this: given the operations of adding vertices, calculate the sum of the weights of all edges of the forest, resulting after the application of all defined operations, modulo $ 1000000007 $ $ (10^{9}+7) $ .

The first line contains a single integer $ n $ $ (1<=n<=10^{5}) $ — the number of operations of adding a vertex. Next $ n $ lines contain descriptions of the operations, the $ i $ -th line contains the description of the operation of adding the $ i $ -th vertex in the following format: the first number of a line is an integer $ k $ $ (0<=k<=i-1) $ , then follow $ 2k $ space-separated integers: $ v_{1},x_{1},v_{2},x_{2},...\ ,v_{k},x_{k} $ $ (1<=v_{j}<=i-1,|x_{j}|<=10^{9}) $ . The operations are given in the order, in which they should be applied to the graph. It is guaranteed that sum $ k $ of all operations does not exceed $ 10^{5} $ , also that applying operations of adding vertexes does not result in loops and multiple edges.

Print a single number — the sum of weights of all edges of the resulting graph modulo $ 1000000007 $ $ (10^{9}+7) $ .

6
0
0
1 2 1
2 1 5 2 2
1 1 2
1 3 4

30

5
0
1 1 5
0
0
2 3 1 4 3

9

Conside the first sample: 1. Vertex $ 1 $ is added. $ k=0 $ , thus no edges are added. 2. Vertex $ 2 $ is added. $ k=0 $ , thus no edges are added. 3. Vertex $ 3 $ is added. $ k=1 $ . $ v_{1}=2 $ , $ x_{1}=1 $ . Edge from vertex $ root(2)=2 $ to vertex $ 3 $ with weight $ depth(2)+x_{1}=0+1=1 $ is added. 4. Vertex $ 4 $ is added. $ k=2 $ . $ v_{1}=1 $ , $ x_{1}=5 $ . Edge from vertex $ root(1)=1 $ to vertex $ 4 $ with weight $ depth(1)+x_{1}=0+5=5 $ is added. $ v_{2}=2 $ , $ x_{2}=2 $ . Edge from vertex $ root(2)=3 $ to vertex $ 4 $ with weight $ depth(2)+x_{1}=1+2=3 $ is added. 5. Vertex $ 5 $ is added. $ k=1 $ . $ v_{1}=1 $ , $ x_{1}=2 $ . Edge from vertex $ root(1)=4 $ to vertex $ 5 $ with weight $ depth(1)+x_{1}=5+2=7 $ is added. 6. Vertex $ 6 $ is added. $ k=1 $ . $ v_{1}=3 $ , $ x_{1}=4 $ . Edge from vertex $ root(3)=5 $ to vertex $ 6 $ with weight $ depth(3)+x_{1}=10+4=14 $ is added. The resulting graph is shown on the pictore below: