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, degreev and sv, 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 degreev and sv 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 degreei and si (0 ≤ degreei ≤ n - 1, 0 ≤ si < 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.

Examples

Input

3
2 3
1 0
1 0


Output

2
1 0
2 0


Input

2
1 1
1 0


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".
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class ProblemA2 {
    BufferedReader rd;

    private ProblemA2() throws IOException {
        rd = new BufferedReader(new InputStreamReader(System.in));
        compute();
    }

    private void compute() throws IOException {
        int n = pint();
        int[] xr = new int[n];
        int[] dg = new int[n];
        for(int i=0;i<n;i++) {
            int[] a = intarr();
            if(a[0] != 0) {
                dg[i] = a[0];
                xr[i] = a[1];
            }
        }
        SetMultiMap<Integer, Integer> edgeMap = new HashSetHashMultiMap<>();
        Queue<Integer> q = new LinkedList<>();
        for(int i=0;i<n;i++) {
            if(dg[i] == 1) {
                q.add(i);
            }
        }
        while(!q.isEmpty()) {
            int v = q.poll();
            if(dg[v] == 1) {
                int next = xr[v];
                if(v != next) {
                    edgeMap.getOrCreate(Math.min(v, next)).add(Math.max(v, next));
                    dg[v]--;
                    dg[next]--;
                    xr[next] ^= v;
                    xr[v] ^= next;
                    if(dg[v] == 1) {
                        q.add(v);
                    }
                    if(dg[next] == 1) {
                        q.add(next);
                    }
                }
            }
        }

        int size = 0;
        for(Map.Entry<Integer, Set<Integer>> e: edgeMap.entrySet()) {
            size += e.getValue().size();
        }

        out(size);
        for(Map.Entry<Integer, Set<Integer>> e: edgeMap.entrySet()) {
            for(Integer s: e.getValue()) {
                out(e.getKey()+" "+s);
            }
        }
    }


    private interface MultiMap<K, V, C> extends Map<K, C> {
        C getOrCreate(K key);
    }

    private interface SetMultiMap<K, V> extends MultiMap<K, V, Set<V>> {
    }

    private static class HashSetHashMultiMap<K, V> extends HashMap<K, Set<V>> implements SetMultiMap<K, V> {

        @Override
        public Set<V> getOrCreate(K key) {
            Set<V> container = get(key);
            if(container == null) {
                container = new HashSet<>();
                put(key, container);
            }
            return container;
        }
    }


    private int pint() throws IOException {
        return pint(rd.readLine());
    }

    private int pint(String s) {
        return Integer.parseInt(s);
    }

    private int[] intarr() throws IOException {
        return intarr(rd.readLine());
    }

    private int[] intarr(String s) {
        String[] q = split(s);
        int n = q.length;
        int[] a = new int[n];
        for(int i=0;i<n;i++) {
            a[i] = Integer.parseInt(q[i]);
        }
        return a;
    }

    private String[] split(String s) {
        int n = s.length();
        int sp = 0;
        for(int i=0;i<n;i++) {
            if(s.charAt(i)==' ') {
                sp++;
            }
        }
        String[] res = new String[sp+1];
        int last = 0;
        int x = 0;
        for(int i=0;i<n;i++) {
            char c = s.charAt(i);
            if(c == ' ') {
                res[x++] = s.substring(last,i);
                last = i+1;
            }
        }
        res[x] = s.substring(last,n);
        return res;
    }

    private static void out(Object x) {
        System.out.println(x);
    }

    public static void main(String[] args) throws IOException {
        new ProblemA2();
    }
}
