Misha and Forest

1000ms

262144K

Description:

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 ≤ 2¹⁶), 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 < 2¹⁶), 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.

Sample Input:

Sample Output:

2
1 0
2 0

Sample Input:

2
1 1
1 0

Sample Output:

1
0 1

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".

Informação

Provedor Codeforces

Código CF501C