Problem: Vasya has an array a_1, a_2, ..., a_n.

You don't know this array, but he told you m facts about this array. The i-th fact is a triple of numbers t_i, l_i and r_i (0 ≤ t_i ≤ 1, 1 ≤ l_i < r_i ≤ n) and it means:

  * if t_i=1 then subbarray a_{l_i}, a_{l_i + 1}, ..., a_{r_i} is sorted in non-decreasing order; 
  * if t_i=0 then subbarray a_{l_i}, a_{l_i + 1}, ..., a_{r_i} is not sorted in non-decreasing order. A subarray is not sorted if there is at least one pair of consecutive elements in this subarray such that the former is greater than the latter. 



For example if a = [2, 1, 1, 3, 2] then he could give you three facts: t_1=1, l_1=2, r_1=4 (the subarray [a_2, a_3, a_4] = [1, 1, 3] is sorted), t_2=0, l_2=4, r_2=5 (the subarray [a_4, a_5] = [3, 2] is not sorted), and t_3=0, l_3=3, r_3=5 (the subarray [a_3, a_5] = [1, 3, 2] is not sorted).

You don't know the array a. Find any array which satisfies all the given facts.

Input

The first line contains two integers n and m (2 ≤ n ≤ 1000, 1 ≤ m ≤ 1000).

Each of the next m lines contains three integers t_i, l_i and r_i (0 ≤ t_i ≤ 1, 1 ≤ l_i < r_i ≤ n).

If t_i = 1 then subbarray a_{l_i}, a_{l_i + 1}, ... , a_{r_i} is sorted. Otherwise (if t_i = 0) subbarray a_{l_i}, a_{l_i + 1}, ... , a_{r_i} is not sorted.

Output

If there is no array that satisfies these facts in only line print NO (in any letter case).

If there is a solution, print YES (in any letter case). In second line print n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the array a, satisfying all the given facts. If there are multiple satisfying arrays you can print any of them.

Examples

Input


7 4
1 1 3
1 2 5
0 5 6
1 6 7


Output


YES
1 2 2 3 5 4 4


Input


4 2
1 1 4
0 2 3


Output


NO

Solution (in JAVA):

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

/**
 * @author kenpen 
 */
public class VasyaArray 
{
    public static void main(String[] args) 
    {
        int n = getInt();
        int m = getInt();
//        int[] arr = new int[n];
//        for (int i = 0 ; i < n ; ++i) arr[i] = -1;
        int [][] facts = new int[m][3];
        List<int[]> decRanges = new ArrayList<>();
        for (int i = 0 ; i < m; ++i) {
            facts[i][0] = getInt();
            facts[i][1] = getInt() - 1;
            facts[i][2] = getInt() - 1;
            if (facts[i][0] == 0) {
                decRanges.add(new int[]{facts[i][1], facts[i][2]});
            }
        }
        int[][] sorted = merge(facts, 1);


        int [] b = new int[n - 1];
        // bi = a(i+1) - ai
        for (int i = 0 ; i < n - 1; ++i) b[i] = -1;
        for (int[] range : sorted) {
            int l = range[0];
            int r = range[1];
            for (int i = l; i < r && i < n - 1; ++i) b[i] = 0;
        }
        boolean fail = false;
        for (int[] range: decRanges) {
            int l = range[0];
            int r = range[1];
            boolean hasDec = false;
            for (int i = l; i < r && i < n - 1; ++i) hasDec = hasDec || b[i] == -1;
            fail = fail || !hasDec;
        }
        if (fail) {
            System.out.println("NO");
            return;
        }
        int[] ans = new int[n];
        ans[0] = 2000;
        for (int i = 1; i < n; ++i) {
            ans[i] = b[i - 1] + ans[i - 1];
        }
        System.out.println("YES");
        System.out.println(arrayToString(ans));
    }


    /**
     * merge the sorted intervals
     */
    private static int[][] merge(int[][] facts, int want)
    {
        List<int[]> list = new ArrayList<>();
        for (int[] fact : facts) {
            if (fact[0] != want) continue;
            list.add(fact);
        }
        int n = list.size();
        if (n == 0) return new int[][]{};
        int[] st = new int[n];
        int[] ed = new int[n];
        for (int i = 0 ; i < list.size(); ++i) {
            st[i] = list.get(i)[1];
            ed[i] = list.get(i)[2];
        }
        Arrays.sort(st);
        Arrays.sort(ed);
        int ls = st[0];
        int le = ed[0];
        List<int[]> merged = new ArrayList<>();
        for (int i = 1 ; i < n ; ++i) {
            if (st[i] <= le) {
                le = ed[i];
            }
            else {
                merged.add(new int[] {ls, le});
                ls = st[i];
                le = ed[i];
            }
        }
        merged.add(new int[]{ls, le});
        return merged.toArray(new int[merged.size()][]);
    }


    // ===== Printing code ===== 
    static StringBuilder buf = new StringBuilder();
    static int bufSize = 5000;
    static void print(String s) {print(s, false);}

    static void print(String s, boolean newLine) {
        buf.append(s);
        if (newLine) buf.append("\n");
        if (buf.length() >= bufSize) {
            System.out.print(buf);
            buf.delete(0, buf.length());
        }
    }
    
    static void flush() { 
        System.out.print(buf); 
        buf.delete(0, buf.length());
    }

    static String arrayToString(int[] arr) {
        StringBuilder sb = new StringBuilder();
        for (int a : arr) sb.append(a).append(" ");
        if (arr.length > 0) sb.deleteCharAt(sb.length() - 1);
        return sb.toString();
    }

    // ===== INPUT TAKING CODE ==== 
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static StringTokenizer st;
    static void checkSt() {
        if (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                System.out.println("Error parsing input");
            }
        }
    }
    static int getInt() {
        checkSt();
        return Integer.valueOf(st.nextToken());
    }

    static long getLong() {
        checkSt();
        return Long.valueOf(st.nextToken());
    }
    

    static long getNewLineLong() {
        try {
            return Long.valueOf(br.readLine());
        } catch (IOException e) {
            System.out.println("Error parsing input");
            return 0;
        }
    }

    static int getNewLineInt() {
        try {
            return Integer.valueOf(br.readLine());
        } catch (IOException e) {
            System.out.println("Error parsing input");
            return 0;
        }
    }

    static char getChar() {
        checkSt();
        return st.nextToken().charAt(0);
    }

    static String getStr() {
        checkSt();
        return st.nextToken();
    }
    
}