Problem: Vus the Cossack has a simple graph with n vertices and m edges. Let d_i be a degree of the i-th vertex. Recall that a degree of the i-th vertex is the number of conected edges to the i-th vertex.

He needs to remain not more than ⌈ (n+m)/(2) ⌉ edges. Let f_i be the degree of the i-th vertex after removing. He needs to delete them in such way so that ⌈ (d_i)/(2) ⌉ ≤ f_i for each i. In other words, the degree of each vertex should not be reduced more than twice. 

Help Vus to remain the needed edges!

Input

The first line contains two integers n and m (1 ≤ n ≤ 10^6, 0 ≤ m ≤ 10^6) — the number of vertices and edges respectively.

Each of the next m lines contains two integers u_i and v_i (1 ≤ u_i, v_i ≤ n) — vertices between which there is an edge.

It is guaranteed that the graph does not have loops and multiple edges.

It is possible to show that the answer always exists.

Output

In the first line, print one integer k (0 ≤ k ≤ ⌈ (n+m)/(2) ⌉) — the number of edges which you need to remain.

In each of the next k lines, print two integers u_i and v_i (1 ≤ u_i, v_i ≤ n) — the vertices, the edge between which, you need to remain. You can not print the same edge more than once.

Examples

Input


6 6
1 2
2 3
3 4
4 5
5 3
6 5


Output


5
2 1
3 2
5 3
5 4
6 5


Input


10 20
4 3
6 5
4 5
10 8
4 8
5 8
10 4
9 5
5 1
3 8
1 2
4 7
1 4
10 7
1 7
6 1
9 6
3 9
7 9
6 2


Output


12
2 1
4 1
5 4
6 5
7 1
7 4
8 3
8 5
9 3
9 6
10 4
10 7

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
class UnionFind {
 private:
 public:
  vector<int> p, rank, setSize, minn;
  int numSets;
  UnionFind(int N) {
    setSize.assign(N, 1);
    numSets = N;
    rank.assign(N, 0);
    p.assign(N, 0);
    minn.resize(N);
    for (int i = 0; i < N; i++) {
      p[i] = i;
      minn[i] = i;
    }
  }
  int findSet(int i) {
    if (p[i] == i)
      return i;
    else {
      p[i] = findSet(p[i]);
      minn[p[i]] = min(minn[p[i]], i);
      return p[i];
    }
  }
  bool isSameSet(int i, int j) { return findSet(i) == findSet(j); }
  void unionSet(int i, int j) {
    if (!isSameSet(i, j)) {
      numSets--;
      int x = findSet(i), y = findSet(j);
      if (rank[x] > rank[y]) {
        p[y] = x;
        setSize[x] += setSize[y];
        minn[x] = min(minn[x], minn[y]);
      } else {
        p[x] = y;
        setSize[y] += setSize[x];
        minn[y] = min(minn[x], minn[y]);
        if (rank[x] == rank[y]) rank[y]++;
      }
    }
  }
  int numDisjointSets() { return numSets; }
  int sizeOfSet(int i) { return setSize[findSet(i)]; }
};
class fenwick_tree {
  vector<long> t;
  long size;

 public:
  fenwick_tree(long n) {
    t.assign(n + 1, 0);
    size = n + 1;
  }
  long LSOne(long k) { return k & (-k); }
  void update(long index, long val) {
    for (; index < size; index += LSOne(index)) t[index] += val;
  }
  long query_full(long a, long b) {
    return query(b) - ((a <= 1) ? 0 : query(a - 1));
  }
  long query(long b) {
    if (b < 1) return 0;
    long sum = 0;
    for (; b; b -= LSOne(b)) sum += t[b];
    return sum;
  }
};
long long gcd(long long a, long long b) {
  while (b != 0) {
    long long t = b;
    b = a % b;
    a = t;
  }
  return a;
}
int prime[1050000];
int lp[3001002];
class prime_class {
 public:
  long top;
  prime_class() {
    int i, i2, j;
    top = 0;
    lp[0] = 0;
    lp[1] = 1;
    for (i = 2; i < 3001002; i++) lp[i] = 0;
    top = 0;
    for (i = 2; i < 3001002; ++i) {
      if (lp[i] == 0) {
        lp[i] = i;
        prime[top++] = i;
      }
      for (j = 0; (j < top) && (prime[j] <= lp[i]) && (i * prime[j] < 3001002);
           ++j)
        lp[i * prime[j]] = prime[j];
    }
  }
  bool isprime(int key) {
    if (key < 3001002)
      return (lp[key] == key) && (key >= 2);
    else {
      int i;
      for (i = 0; (i < top) && (prime[i] * prime[i] <= key); i++)
        if (key % prime[i] == 0) return false;
      return true;
    }
  }
  unordered_map<int, int> factorize(int key) {
    unordered_map<int, int> ans;
    while (lp[key] != key) {
      ans[lp[key]]++;
      key /= lp[key];
    }
    if (key > 1) ans[key]++;
    return ans;
  }
  vector<pair<long long, long long>> factorize_full(long long key) {
    vector<pair<long long, long long>> ans;
    long i, ct;
    for (i = 0; (i < top) && (prime[i] <= key); i++)
      if (key % prime[i] == 0) {
        ct = 0;
        while (key % prime[i] == 0) {
          ct++;
          key /= prime[i];
        }
        ans.push_back({prime[i], ct});
      }
    if (key > 1) {
      ans.push_back({key, 1});
    }
    return ans;
  }
  void generate_divisors(int step, int v, vector<pair<int, int>>& fp,
                         vector<int>& ans) {
    if (step < fp.size()) {
      generate_divisors(step + 1, v, fp, ans);
      for (int i = 1; i <= fp[step].second; i++) {
        v *= fp[step].first;
        generate_divisors(step + 1, v, fp, ans);
      }
    } else
      ans.push_back(v);
  }
  void generate_divisors_full(long long step, long long v,
                              vector<pair<long long, long long>>& fp,
                              vector<long long>& ans) {
    if (step < fp.size()) {
      generate_divisors_full(step + 1, v, fp, ans);
      for (int i = 1; i <= fp[step].second; i++) {
        v *= fp[step].first;
        generate_divisors_full(step + 1, v, fp, ans);
      }
    } else
      ans.push_back(v);
  }
  vector<int> get_divisors(int key) {
    unordered_map<int, int> f = factorize(key);
    int n = f.size();
    vector<pair<int, int>> fp;
    for (auto p : f) fp.push_back(p);
    vector<int> ans;
    generate_divisors(0, 1, fp, ans);
    return ans;
  }
  vector<long long> get_divisors_full(long long key) {
    vector<pair<long long, long long>> f = factorize_full(key);
    int n = f.size();
    vector<pair<long long, long long>> fp;
    for (auto p : f) fp.push_back(p);
    vector<long long> ans;
    generate_divisors_full(0, 1, fp, ans);
    return ans;
  }
};
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, m, i, j, k, a, b, mm;
  cin >> n >> m;
  vector<pair<pair<int, int>, pair<int, int>>> e(m);
  vector<int> d(n + 1, 0), f;
  vector<bool> keep(m, true);
  for (i = 0; i < m; i++) {
    cin >> a >> b;
    e[i].second = {a, b};
    d[a]++;
    d[b]++;
  }
  for (i = 0; i < m; i++) {
    a = e[i].second.first;
    b = e[i].second.second;
    e[i].first = {max(d[a], d[b]), rand() % 1000};
  }
  sort(e.rbegin(), e.rend());
  f = d;
  mm = m;
  for (i = 0; i < m; i++) {
    a = e[i].second.first;
    b = e[i].second.second;
    if ((f[a] - 1 >= (d[a] + 1) / 2) && (f[b] - 1 >= (d[b] + 1) / 2)) {
      keep[i] = false;
      f[a]--;
      f[b]--;
      mm--;
    }
  }
  cout << mm << "\n";
  for (i = 0; i < m; i++) {
    if (keep[i]) cout << e[i].second.first << " " << e[i].second.second << "\n";
  }
  return 0;
}