#include <bits/stdc++.h>
using namespace std;
const pair<long long, long long> NO_PROP = {-1, -1};
class SegTree {
 public:
  pair<long long, long long> maxi;
  pair<long long, long long> toProp = NO_PROP;
  SegTree *left, *right;
  long long lx, rx;
  SegTree(long long l, long long r) {
    lx = l;
    rx = r;
    maxi = {0, -1};
    toProp = NO_PROP;
    left = NULL, right = NULL;
  }
  SegTree* getLeft() {
    assert(lx != rx);
    long long mid = (lx + rx) / 2;
    if (!left) left = new SegTree(lx, mid);
    return left;
  }
  SegTree* getRight() {
    assert(lx != rx);
    long long mid = (lx + rx) / 2;
    if (!right) right = new SegTree(mid + 1, rx);
    return right;
  }
  void prop() {
    if (lx != rx && toProp != NO_PROP) {
      getLeft()->toProp = toProp;
      getRight()->toProp = toProp;
      if (getLeft()->maxi.first < toProp.first) {
        getLeft()->maxi = toProp;
      }
      if (getRight()->maxi.first < toProp.first) {
        getRight()->maxi = toProp;
      }
      toProp = NO_PROP;
    }
  }
  void rangeUpdate(long long l, long long r, pair<long long, long long> val) {
    this->prop();
    if (rx < l || r < lx) return;
    if (l <= lx && rx <= r) {
      if (maxi.first <= val.first) {
        maxi = val;
      }
      toProp = val;
      return;
    }
    getLeft()->rangeUpdate(l, r, val);
    getRight()->rangeUpdate(l, r, val);
    maxi = max(getLeft()->maxi, getRight()->maxi);
  }
  pair<long long, long long> rangeVal(long long l, long long r) {
    this->prop();
    if (rx < l || r < lx) return {0, -1};
    if (l <= lx && rx <= r) {
      return maxi;
    }
    auto a = getLeft()->rangeVal(l, r);
    auto b = getRight()->rangeVal(l, r);
    return max(a, b);
  }
};
void pilot() {
  long long n, m;
  cin >> n >> m;
  vector<vector<pair<long long, long long>>> a(n);
  vector<long long> tmp;
  for (long long i = 0; i < m; i++) {
    long long row, l, r;
    cin >> row >> l >> r;
    tmp.push_back(l);
    tmp.push_back(r);
    a[row - 1].push_back({l, r});
  }
  sort(tmp.begin(), tmp.end());
  map<long long, long long> actualToCompressedCoords;
  long long siz = tmp.size();
  for (int i = 0; i < siz;) {
    int j = i;
    while (j < siz && tmp[i] == tmp[j]) j++;
    actualToCompressedCoords[tmp[i]] = i;
    i = j;
  }
  auto segTree = new SegTree(0, 1e9);
  vector<long long> dp(n), parent(n, -1);
  vector<long long> ans;
  for (long long i = 0; i < n; i++) {
    pair<long long, long long> val = {0, -1};
    for (auto& seg : a[i]) {
      long long l = actualToCompressedCoords[seg.first];
      long long r = actualToCompressedCoords[seg.second];
      auto tmp = segTree->rangeVal(l, r);
      val = max(val, tmp);
    }
    dp[i] = val.first + 1;
    parent[i] = val.second;
    for (auto& seg : a[i]) {
      long long l = actualToCompressedCoords[seg.first];
      long long r = actualToCompressedCoords[seg.second];
      segTree->rangeUpdate(l, r, {val.first + 1, i});
    }
  }
  int maxiIndx = 0;
  for (int i = 0; i < n; i++) {
    if (dp[i] > dp[maxiIndx]) {
      maxiIndx = i;
    }
  }
  vector<long long> visited(n);
  while (parent[maxiIndx] != -1) {
    visited[maxiIndx] = 1;
    maxiIndx = parent[maxiIndx];
  }
  visited[maxiIndx] = 1;
  for (int i = 0; i < n; i++) {
    if (!visited[i]) ans.push_back(i + 1);
  }
  cout << ans.size() << "\n";
  for (int x : ans) cout << x << " ";
  cout << "\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long tt = 1;
  for (long long i = 0; i < tt; i++) {
    pilot();
  }
  return 0;
}

### Prompt

Create a solution in cpp for the following problem:

Moamen was drawing a grid of n rows and 10^9 columns containing only digits 0 and 1. Ezzat noticed what Moamen was drawing and became interested in the minimum number of rows one needs to remove to make the grid beautiful.

A grid is beautiful if and only if for every two consecutive rows there is at least one column containing 1 in these two rows.

Ezzat will give you the number of rows n, and m segments of the grid that contain digits 1. Every segment is represented with three integers i, l, and r, where i represents the row number, and l and r represent the first and the last column of the segment in that row.

For example, if n = 3, m = 6, and the segments are (1,1,1), (1,7,8), (2,7,7), (2,15,15), (3,1,1), (3,15,15), then the grid is:

<image>

Your task is to tell Ezzat the minimum number of rows that should be removed to make the grid beautiful.

Input

The first line contains two integers n and m (1 ≤ n, m ≤ 3⋅10^5).

Each of the next m lines contains three integers i, l, and r (1 ≤ i ≤ n, 1 ≤ l ≤ r ≤ 10^9). Each of these m lines means that row number i contains digits 1 in columns from l to r, inclusive.

Note that the segments may overlap.

Output

In the first line, print a single integer k — the minimum number of rows that should be removed.

In the second line print k distinct integers r_1, r_2, …, r_k, representing the rows that should be removed (1 ≤ r_i ≤ n), in any order.

If there are multiple answers, print any.

Examples

Input


3 6
1 1 1
1 7 8
2 7 7
2 15 15
3 1 1
3 15 15


Output


0


Input


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


Output


3
2 4 5

Note

In the first test case, the grid is the one explained in the problem statement. The grid has the following properties: 

  1. The 1-st row and the 2-nd row have a common 1 in the column 7. 
  2. The 2-nd row and the 3-rd row have a common 1 in the column 15. 

As a result, this grid is beautiful and we do not need to remove any row.

In the second test case, the given grid is as follows: 

<image>

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const pair<long long, long long> NO_PROP = {-1, -1};
class SegTree {
 public:
  pair<long long, long long> maxi;
  pair<long long, long long> toProp = NO_PROP;
  SegTree *left, *right;
  long long lx, rx;
  SegTree(long long l, long long r) {
    lx = l;
    rx = r;
    maxi = {0, -1};
    toProp = NO_PROP;
    left = NULL, right = NULL;
  }
  SegTree* getLeft() {
    assert(lx != rx);
    long long mid = (lx + rx) / 2;
    if (!left) left = new SegTree(lx, mid);
    return left;
  }
  SegTree* getRight() {
    assert(lx != rx);
    long long mid = (lx + rx) / 2;
    if (!right) right = new SegTree(mid + 1, rx);
    return right;
  }
  void prop() {
    if (lx != rx && toProp != NO_PROP) {
      getLeft()->toProp = toProp;
      getRight()->toProp = toProp;
      if (getLeft()->maxi.first < toProp.first) {
        getLeft()->maxi = toProp;
      }
      if (getRight()->maxi.first < toProp.first) {
        getRight()->maxi = toProp;
      }
      toProp = NO_PROP;
    }
  }
  void rangeUpdate(long long l, long long r, pair<long long, long long> val) {
    this->prop();
    if (rx < l || r < lx) return;
    if (l <= lx && rx <= r) {
      if (maxi.first <= val.first) {
        maxi = val;
      }
      toProp = val;
      return;
    }
    getLeft()->rangeUpdate(l, r, val);
    getRight()->rangeUpdate(l, r, val);
    maxi = max(getLeft()->maxi, getRight()->maxi);
  }
  pair<long long, long long> rangeVal(long long l, long long r) {
    this->prop();
    if (rx < l || r < lx) return {0, -1};
    if (l <= lx && rx <= r) {
      return maxi;
    }
    auto a = getLeft()->rangeVal(l, r);
    auto b = getRight()->rangeVal(l, r);
    return max(a, b);
  }
};
void pilot() {
  long long n, m;
  cin >> n >> m;
  vector<vector<pair<long long, long long>>> a(n);
  vector<long long> tmp;
  for (long long i = 0; i < m; i++) {
    long long row, l, r;
    cin >> row >> l >> r;
    tmp.push_back(l);
    tmp.push_back(r);
    a[row - 1].push_back({l, r});
  }
  sort(tmp.begin(), tmp.end());
  map<long long, long long> actualToCompressedCoords;
  long long siz = tmp.size();
  for (int i = 0; i < siz;) {
    int j = i;
    while (j < siz && tmp[i] == tmp[j]) j++;
    actualToCompressedCoords[tmp[i]] = i;
    i = j;
  }
  auto segTree = new SegTree(0, 1e9);
  vector<long long> dp(n), parent(n, -1);
  vector<long long> ans;
  for (long long i = 0; i < n; i++) {
    pair<long long, long long> val = {0, -1};
    for (auto& seg : a[i]) {
      long long l = actualToCompressedCoords[seg.first];
      long long r = actualToCompressedCoords[seg.second];
      auto tmp = segTree->rangeVal(l, r);
      val = max(val, tmp);
    }
    dp[i] = val.first + 1;
    parent[i] = val.second;
    for (auto& seg : a[i]) {
      long long l = actualToCompressedCoords[seg.first];
      long long r = actualToCompressedCoords[seg.second];
      segTree->rangeUpdate(l, r, {val.first + 1, i});
    }
  }
  int maxiIndx = 0;
  for (int i = 0; i < n; i++) {
    if (dp[i] > dp[maxiIndx]) {
      maxiIndx = i;
    }
  }
  vector<long long> visited(n);
  while (parent[maxiIndx] != -1) {
    visited[maxiIndx] = 1;
    maxiIndx = parent[maxiIndx];
  }
  visited[maxiIndx] = 1;
  for (int i = 0; i < n; i++) {
    if (!visited[i]) ans.push_back(i + 1);
  }
  cout << ans.size() << "\n";
  for (int x : ans) cout << x << " ";
  cout << "\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long tt = 1;
  for (long long i = 0; i < tt; i++) {
    pilot();
  }
  return 0;
}

```