CF856D.Masha and Cactus

Masha is fond of cacti. When she was a little girl, she decided to plant a tree. Now Masha wants to make a nice cactus out of her tree.

Recall that tree is a connected undirected graph that has no cycles. Cactus is a connected undirected graph such that each vertex belongs to at most one cycle.

Masha has some additional edges that she can add to a tree. For each edge she knows which vertices it would connect and the beauty of this edge. Masha can add some of these edges to the graph if the resulting graph is a cactus. Beauty of the resulting cactus is sum of beauties of all added edges.

Help Masha find out what maximum beauty of the resulting cactus she can achieve.

玛莎非常喜欢仙人掌。小时候，她决定种一棵树。现在，玛莎想将她的树改造成一棵漂亮的仙人掌。

回忆一下：树是一个连通的无向图，且不含环；仙人掌是一个连通的无向图，其中每个顶点至多属于一个环。

玛莎拥有一些额外的边，她可以将这些边添加到树中。对于每条边，她知道该边所连接的两个顶点以及该边的“美丽值”（beauty）。玛莎可以向图中添加其中若干条边，但要求添加后的图仍是一棵仙人掌。最终仙人掌的美丽值等于所有被添加边的美丽值之和。

请帮助玛莎计算：她所能得到的仙人掌的最大美丽值是多少？

The first line of the input data contains two integers n and m — the number of vertices in a tree, and the number of additional edges available (3 ≤ n ≤ 2·105; 0 ≤ m ≤ 2·105).

Let us describe Masha's tree. It has a root at vertex 1. The second line contains n - 1 integers: _p_2, _p_3, ..., p__n, here p__i — is the parent of a vertex i — the first vertex on a path from the vertex i to the root of the tree (1 ≤ p__i < i).

The following m lines contain three integers u__i, v__i and c__i — pairs of vertices to be connected by the additional edges that Masha can add to the tree and beauty of edge (1 ≤ u__i, v__i ≤ n; u__i ≠ v__i; 1 ≤ c__i ≤ 104).

It is guaranteed that no additional edge coincides with the edge of the tree.

输入数据的第一行包含两个整数 $n$ 和 $m$ —— 分别表示树中顶点的数量以及可添加的额外边的数量（$3 \leq n \leq 2\cdot10^5$；$0 \leq m \leq 2\cdot10^5$）。

下面描述玛莎的树：该树以顶点 $1$ 为根。第二行包含 $n-1$ 个整数：$p_2,\,p_3,\,\dots,\,p_n$，其中 $p_i$ 表示顶点 $i$ 的父节点 —— 即从顶点 $i$ 到树根路径上的第一个顶点（$1 \leq p_i < i$）。

接下来的 $m$ 行每行包含三个整数 $u_i$、$v_i$ 和 $c_i$ —— 表示玛莎可以添加到树中的额外边所连接的两个顶点，以及该边的美观度（$1 \leq u_i,\,v_i \leq n$；$u_i \neq v_i$；$1 \leq c_i \leq 10^4$）。

保证任意一条额外边均不与树中已有的边重合。

Output one integer — the maximum beauty of a cactus Masha can achieve.

输出一个整数——玛莎能够达到的仙人掌的最大美观度。