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.
def main():
    import sys
    
    n, tokens = [int(i) for i in sys.stdin.read().split()]
    tokens.reverse()
    
    n = tokens.pop()
    vertices = [[tokens.pop(), tokens.pop()] for i in range(n)]
    
    l = []
    for i in range(n):
        if vertices[i][0] == 1:
            l.append(i)
    
    result = []
    while l:
        v = l.pop()
        u = vertices[v][1]
        result.append((v, u))
        vertices[u][0] -= 1
        vertices[u][1] ^= v
        if vertices[u][0] == 1:
            l.append(u)
    
    print(len(result))
    print('\n'.join(' '.join(str(j) for j in i) for i in result))


main()
