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*<sub class="lower-index">*v*</sub> and *s*<sub class="lower-index">*v*</sub>, 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*<sub class="lower-index">*v*</sub> and *s*<sub class="lower-index">*v*</sub> 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<sup class="upper-index">16</sup>), the number of vertices in the graph.

The *i*-th of the next lines contains numbers *degree*<sub class="lower-index">*i*</sub> and *s*<sub class="lower-index">*i*</sub> (0 ≤ *degree*<sub class="lower-index">*i*</sub> ≤ *n* - 1, 0 ≤ *s*<sub class="lower-index">*i*</sub> &lt; 2<sup class="upper-index">16</sup>), separated by a space.
import sys
import collections
import functools
import operator


hs = []
for _ in range(int(sys.stdin.readline())):

    hs.append(tuple(map(int, sys.stdin.readline().split())))

g = collections.defaultdict(list)
nodes = []
changes = True
while changes:

    changes = False
    for i, (degree, v) in enumerate(hs):

        if degree - len(g[i]) == 1:

            if g[i]:

                v ^= functools.reduce(operator.xor, g[i])

            g[i].append(v)
            g[v].append(i)
            nodes.append((i, v))
            changes = True

print(len(nodes))
for a, b in nodes:

    print(a, b)
