Happy Tree

There is a tree with $N$ vertices numbered 1 to $N$, rooted at vertex 1. Every vertex and every edge carries one number. Write $a_u$ for the number on vertex $u$, and $\mathrm{dist}(v, u)$ for the sum of the numbers on the edges along the path from $v$ to $u$.

A vertex $v$ is sad if the subtree rooted at $v$ contains at least one vertex $u$ with $\mathrm{dist}(v, u) > a_u$. A tree with no sad vertex is a happy tree.

Minju cannot lift anything heavier than a keyboard, so she can cut leaves only. A leaf is a vertex with no child, that is, a vertex whose only neighbour is its parent. The root is a leaf only when it is the last vertex left in the tree. Cutting a vertex removes it from the tree, and a vertex that becomes a leaf as a result can be cut next.

Find the minimum number of vertices Minju has to cut to make the tree happy.

In the tree drawn as 1) below, the 5 vertices marked 2) to 6) have to be cut.

The first line contains the number of vertices $N$ ($1 \le N \le 100\,000$).

The second line contains $a_1, a_2, \ldots, a_N$ ($1 \le a_i \le 1\,000\,000\,000$), the numbers written on vertices 1 to $N$, separated by spaces.

Each of the next $N - 1$ lines contains two integers. Line $i$ contains $p_i$ ($1 \le p_i \le N$) and $c_i$ ($-1\,000\,000\,000 \le c_i \le 1\,000\,000\,000$), meaning that vertex $i + 1$ and vertex $p_i$ are joined by an edge whose number is $c_i$. The given edges always form a tree.

$p_i$ can be larger than $i + 1$, so you have to work out the parent and child relations yourself by rooting the tree at vertex 1.

Print the minimum number of leaves that have to be cut to make the tree happy, on one line.