Problem: There are N squares arranged in a row. The squares are numbered 1, 2, ..., N, from left to right.

Snuke is painting each square in red, green or blue. According to his aesthetic sense, the following M conditions must all be satisfied. The i-th condition is:

* There are exactly x_i different colors among squares l_i, l_i + 1, ..., r_i.



In how many ways can the squares be painted to satisfy all the conditions? Find the count modulo 10^9+7.

Constraints

* 1 ≤ N ≤ 300
* 1 ≤ M ≤ 300
* 1 ≤ l_i ≤ r_i ≤ N
* 1 ≤ x_i ≤ 3

Input

Input is given from Standard Input in the following format:


N M
l_1 r_1 x_1
l_2 r_2 x_2
:
l_M r_M x_M


Output

Print the number of ways to paint the squares to satisfy all the conditions, modulo 10^9+7.

Examples

Input

3 1
1 3 3


Output

6


Input

4 2
1 3 1
2 4 2


Output

6


Input

1 3
1 1 1
1 1 2
1 1 3


Output

0


Input

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


Output

108

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

class Lrx {
  final int l, r, x;

  Lrx(int l, int r, int x) {
    this.l = l;
    this.r = r;
    this.x = x;
  }
}

public class Main {
  private static long solve(int n, int m, int[][] lrxs) {
    List<List<Lrx>> matrix = new ArrayList<>();
    for (int i = 0; i <= n + 1; i++) {
      matrix.add(new ArrayList<>());
    }
    for (int[] lrx : lrxs) {
      int l = lrx[0];
      int r = lrx[1];
      int x = lrx[2];
      if (r - l + 1 < x) {
        return 0;
      }
      matrix.get(r).add(new Lrx(l, r, x));
    }

    ModCalculator mc = new ModCalculator(1_000_000_007L);
    long[][] dptable = new long[n + 1][n + 1];
    dptable[0][0] = 3;
    for (int i = 2; i <= n; i++) {
      long[][] nextDptable = new long[n + 1][n + 1];
      for (int maxLeftIndexWith2Colors = 0; maxLeftIndexWith2Colors <= i; maxLeftIndexWith2Colors++) {
        for (int maxLeftIndexWith3Colors = 0; maxLeftIndexWith3Colors <= i; maxLeftIndexWith3Colors++) {
          long v = dptable[maxLeftIndexWith2Colors][maxLeftIndexWith3Colors];
          nextDptable[maxLeftIndexWith2Colors][maxLeftIndexWith3Colors] = mc.add(nextDptable[maxLeftIndexWith2Colors][maxLeftIndexWith3Colors], v);
          nextDptable[i - 1][maxLeftIndexWith3Colors] = mc.add(nextDptable[i - 1][maxLeftIndexWith3Colors], v);
          nextDptable[i - 1][maxLeftIndexWith2Colors] = mc.add(nextDptable[i - 1][maxLeftIndexWith2Colors], v);
        }
      }
      dptable = nextDptable;
      for (Lrx lrx : matrix.get(i)) {
        switch (lrx.x) {
          case 1: {
            for (int maxLeftIndexWith2Colors = lrx.l; maxLeftIndexWith2Colors <= i; maxLeftIndexWith2Colors++) {
              for (int maxLeftIndexWith3Colors = 0; maxLeftIndexWith3Colors <= i; maxLeftIndexWith3Colors++) {
                dptable[maxLeftIndexWith2Colors][maxLeftIndexWith3Colors] = 0;
              }
            }
            break;
          }
          case 2: {
            for (int maxLeftIndexWith2Colors = 0; maxLeftIndexWith2Colors < lrx.l; maxLeftIndexWith2Colors++) {
              for (int maxLeftIndexWith3Colors = 0; maxLeftIndexWith3Colors <= i; maxLeftIndexWith3Colors++) {
                dptable[maxLeftIndexWith2Colors][maxLeftIndexWith3Colors] = 0;
              }
            }
            for (int maxLeftIndexWith2Colors = 0; maxLeftIndexWith2Colors <= i; maxLeftIndexWith2Colors++) {
              for (int maxLeftIndexWith3Colors = lrx.l; maxLeftIndexWith3Colors <= i; maxLeftIndexWith3Colors++) {
                dptable[maxLeftIndexWith2Colors][maxLeftIndexWith3Colors] = 0;
              }
            }
            break;
          }
          case 3: {
            for (int maxLeftIndexWith2Colors = 0; maxLeftIndexWith2Colors <= i; maxLeftIndexWith2Colors++) {
              for (int maxLeftIndexWith3Colors = 0; maxLeftIndexWith3Colors < lrx.l; maxLeftIndexWith3Colors++) {
                dptable[maxLeftIndexWith2Colors][maxLeftIndexWith3Colors] = 0;
              }
            }
            break;
          }
        }
      }
    }
    long answer = 0;
    for (int maxLeftIndexWith2Colors = 0; maxLeftIndexWith2Colors <= n; maxLeftIndexWith2Colors++) {
      for (int maxLeftIndexWith3Colors = 0; maxLeftIndexWith3Colors <= n; maxLeftIndexWith3Colors++) {
        answer = mc.add(answer, dptable[maxLeftIndexWith2Colors][maxLeftIndexWith3Colors]);
      }
    }
    return answer;
  }

  private static void execute(ContestReader reader, ContestWriter out) {
    int n = reader.nextInt();
    int m = reader.nextInt();
    int[][] lrxs = reader.nextInt(m, 3);
    out.println(solve(n, m, lrxs));
  }
  
  public static void main(String[] args) {
    ContestReader reader = new ContestReader(System.in);
    ContestWriter out = new ContestWriter(System.out);
    execute(reader, out);
    out.flush();
  }
}

class ModCalculator {
  private final long mod;
  private final ModCombinationCache modCombinationCache;
  
  ModCalculator(long mod) {
    this.mod = mod;
    this.modCombinationCache = new ModCombinationCache();
  }
  
  public long norm(long v) {
    return v % mod;
  }
  
  public long add(long a, long b) {
    return norm(a + b);
  }
  
  public long sub(long a, long b) {
    return norm(a - b + mod);
  }
  
  public long mul(long a, long b) {
    return norm(a * b);
  }
  
  public long pow(long a, long b) {
    if (b == 0) {
      return 1;
    }
    long v = pow(mul(a, a), b / 2);
    if (b % 2 == 1) {
      return mul(v, a);
    } else {
      return v;
    }
  }
  
  public long inverse(long a) {
    return pow(a, mod - 2);
  }
  
  public long div(long a, long b) {
    return mul(a, inverse(b));
  }

  // Verify ARC 042 D
  // https://atcoder.jp/contests/arc042/tasks/arc042_d
  // a^x mod p === b
  // return -1 there is no such positive x
  public long log(long a, long b) {
    Map<Long, Long> map = new HashMap<>();
    long powA = 1;
    long rootP = 0;
    while (true) {
      if (powA == b && rootP != 0) {
        return rootP;
      }
      if (map.containsKey(powA)) {
        return -1;
      }
      map.put(powA, rootP);
      powA = mul(powA, a);
      rootP++;
      if (rootP * rootP > mod) {
        break;
      }
    }
    long inversePowA = inverse(powA);
    for (int i = 1; i <= rootP; i++) {
      b = mul(b, inversePowA);
      Long value = map.get(b);
      if (value != null && value + rootP * i > 0) {
        return value + rootP * i;
      }
    }
    return -1;
  }
  
  public long getF(int n) {
    return modCombinationCache.getF(n);
  }
  
  public long getP(int n, int r) {
    return modCombinationCache.getP(n, r);
  }
  
  public long getC(int n, int k) {
    return modCombinationCache.getC(n, k);
  }
  
  class ModCombinationCache {
    private final List<Long> factorialCache;
    private final List<Long> factorialInverseCache;
    
    public ModCombinationCache() {
      factorialCache = new ArrayList<>();
      factorialCache.add(1L);
      factorialInverseCache = new ArrayList<>();
      factorialInverseCache.add(1L);
    }
    
    private void resize(int n) {
      for (int i = factorialCache.size() - 1; i < n; i++) {
        long v = mul(factorialCache.get(i), i + 1);
        factorialCache.add(v);
        factorialInverseCache.add(inverse(v));
      }
    }
    
    long getF(int n) {
      resize(n);
      return factorialCache.get(n);
    }
    
    long getP(int n, int r) {
      resize(n);
      return mul(factorialCache.get(n), factorialInverseCache.get(n - r));
    }
    
    long getC(int n, int k) {
      resize(n);
      return mul(factorialCache.get(n), mul(factorialInverseCache.get(k), factorialInverseCache.get(n-k)));
    }
  }
}

class ContestWriter extends PrintWriter {
  ContestWriter(PrintStream printeStream) {
    super(printeStream);
  }

  public void printList(List<? extends Object> list) {
    for (Object object : list) {
      println(object);
    }
  }

  public void printListOneLine(List<? extends Object> list) {
    List<String> stringList = new ArrayList<>();
    for (Object object : list) {
      stringList.add(object.toString());
    }
    println(String.join(" ", stringList));
  }
}

class ContestReader {
  private static final int BUFFER_SIZE = 1024;
  
  private final InputStream stream;
  private final byte[] buffer;
  private int pointer;
  private int bufferLength;
  
  ContestReader(InputStream stream) {
    this.stream = stream;
    this.buffer = new byte[BUFFER_SIZE];
    this.pointer = 0;
    this.bufferLength = 0;
  }
  
  private boolean hasNextByte() {
    if (pointer < bufferLength) {
      return true;
    }
    
    pointer = 0;
    try {
      bufferLength = stream.read(buffer);
    } catch (IOException e) {
      throw new RuntimeException(e);
    }
    return bufferLength > 0;
  }
  
  private int readByte() {
    if (hasNextByte()) {
      return buffer[pointer++];
    } else {
      return -1;
    }
  }
  
  private static boolean isPrintableChar(int c) {
    return 33 <= c && c <= 126;
  }
  
  public boolean hasNext() {
    while (hasNextByte() && !isPrintableChar(buffer[pointer])) {
      pointer++;
    }
    return hasNextByte();
  }
  
  public String next() {
    if (!hasNext()) {
      throw new NoSuchElementException();
    }
    StringBuilder sb = new StringBuilder();
    while(true) {
      int b = readByte();
      if (!isPrintableChar(b)) {
        break;
      }
      sb.appendCodePoint(b);
    }
    return sb.toString();
  }
  
  public String nextLine() {
    if (!hasNext()) {
      throw new NoSuchElementException();
    }
    StringBuilder sb = new StringBuilder();
    while(true) {
      int b = readByte();
      if (!isPrintableChar(b) && b != 0x20) {
        break;
      }
      sb.appendCodePoint(b);
    }
    return sb.toString();
  }
  
  public char nextChar() {
    return next().charAt(0);
  }
  
  public int nextInt() {
    if (!hasNext()) {
      throw new NoSuchElementException();
    }
    
    int n = 0;
    boolean minus = false;
    
    {
      int b = readByte();
      if (b == '-') {
        minus = true;
      } else if ('0' <= b && b <= '9') {
        n = b - '0';
      } else {
        throw new NumberFormatException();
      }
    }
    
    while(true){
      int b = readByte();
      if ('0' <= b && b <= '9') {
        n *= 10;
        n += b - '0';
      } else if (b == -1 || !isPrintableChar(b)) {
        return minus ? -n : n;
      } else {
        throw new NumberFormatException();
      }
    }
  }
  
  public long nextLong() {
    if (!hasNext()) {
      throw new NoSuchElementException();
    }
    
    long n = 0;
    boolean minus = false;
    
    {
      int b = readByte();
      if (b == '-') {
        minus = true;
      } else if ('0' <= b && b <= '9') {
        n = b - '0';
      } else {
        throw new NumberFormatException();
      }
    }
    
    while(true){
      int b = readByte();
      if ('0' <= b && b <= '9') {
        n *= 10;
        n += b - '0';
      } else if (b == -1 || !isPrintableChar(b)) {
        return minus ? -n : n;
      } else {
        throw new NumberFormatException();
      }
    }
  }
  
  public double nextDouble() {
    return Double.parseDouble(next());
  }
  
  public String[] next(int n) {
    String[] array = new String[n];
    for (int i = 0; i < n; i++) {
      array[i] = next();
    }
    return array;
  }
  
  public String[] nextLine(int n) {
    String[] array = new String[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextLine();
    }
    return array;
  }
  
  public char[] nextChar(int n) {
    char[] array = new char[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextChar();
    }
    return array;
  }
  
  public int[] nextInt(int n) {
    int[] array = new int[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextInt();
    }
    return array;
  }
  
  public long[] nextLong(int n) {
    long[] array = new long[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextLong();
    }
    return array;
  }
  
  public double[] nextDouble(int n) {
    double[] array = new double[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextDouble();
    }
    return array;
  }
  
  public char[] nextCharArray() {
    return next().toCharArray();
  }
  
  public String[][] next(int n, int m) {
    String[][] matrix = new String[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = next();
      }
    }
    return matrix;
  }
  
  public int[][] nextInt(int n, int m) {
    int[][] matrix = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextInt();
      }
    }
    return matrix;
  }
  
  public char[][] nextChar(int n, int m) {
    char[][] matrix = new char[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextChar();
      }
    }
    return matrix;
  }
  
  public long[][] nextLong(int n, int m) {
    long[][] matrix = new long[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextLong();
      }
    }
    return matrix;
  }
  
  public double[][] nextDouble(int n, int m) {
    double[][] matrix = new double[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextDouble();
      }
    }
    return matrix;
  }
  
  public char[][] nextCharArray(int n) {
    char[][] matrix = new char[n][];
    for (int i = 0; i < n; i++) {
      matrix[i] = next().toCharArray();
    }
    return matrix;
  }
}