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.

Input

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.

Output

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.

Note

The XOR sum of numbers is the result of bitwise adding numbers modulo $2$. This operation exists in many modern programming languages. For example, in languages C++, Java and Python it is represented as "^", and in Pascal — as "xor".