A9686 | Misha and Forest

Let's define a forest as a non-directed acyclic graph (also without loops and parallel edges). One day Misha played with the forest consisting of $n$ vertices. For each vertex $v$ from $0$ to $n-1$ he wrote down two integers, $degree_{v}$ and $s_{v}$ , were the first integer is the number of vertices adjacent to vertex $v$ , and the second integer is the XOR sum of the numbers of vertices adjacent to $v$ (if there were no adjacent vertices, he wrote down $0$ ).

Next day Misha couldn't remember what graph he initially had. Misha has values $degree_{v}$ and $s_{v}$ left, though. Help him find the number of edges and the edges of the initial graph. It is guaranteed that there exists a forest that corresponds to the numbers written by Misha.

The first line contains integer $n$ ( $1<=n<=2^{16}$ ), the number of vertices in the graph.

The $i$ -th of the next lines contains numbers $degree_{i}$ and $s_{i}$ ( $0<=degree_{i}<=n-1$ , $0<=s_{i}<2^{16}$ ), separated by a space.

In the first line print number $m$ , the number of edges of the graph.

Next print $m$ lines, each containing two distinct numbers, $a$ and $b$ ( $0<=a<=n-1$ , $0<=b<=n-1$ ), corresponding to edge $(a,b)$ .

Edges can be printed in any order; vertices of the edge can also be printed in any order.