Problem: You are given an undirected graph where each edge has one of two colors: black or red.

Your task is to assign a real number to each node so that: 

  * for each black edge the sum of values at its endpoints is 1; 
  * for each red edge the sum of values at its endpoints is 2; 
  * the sum of the absolute values of all assigned numbers is the smallest possible. 



Otherwise, if it is not possible, report that there is no feasible assignment of the numbers.

Input

The first line contains two integers N (1 ≤ N ≤ 100 000) and M (0 ≤ M ≤ 200 000): the number of nodes and the number of edges, respectively. The nodes are numbered by consecutive integers: 1, 2, …, N.

The next M lines describe the edges. Each line contains three integers a, b and c denoting that there is an edge between nodes a and b (1 ≤ a, b ≤ N) with color c (1 denotes black, 2 denotes red).

Output

If there is a solution, the first line should contain the word "YES" and the second line should contain N space-separated numbers. For each i (1 ≤ i ≤ N), the i-th number should be the number assigned to the node i.

Output should be such that: 

  * the sum of the numbers at the endpoints of each edge differs from the precise value by less than 10^{-6}; 
  * the sum of the absolute values of all assigned numbers differs from the smallest possible by less than 10^{-6}. 



If there are several valid solutions, output any of them.

If there is no solution, the only line should contain the word "NO".

Scoring

Subtasks: 

  1. (5 points) N ≤ 5, M ≤ 14 
  2. (12 points) N ≤ 100 
  3. (17 points) N ≤ 1000 
  4. (24 points) N ≤ 10 000 
  5. (42 points) No further constraints 

Examples

Input


4 4
1 2 1
2 3 2
1 3 2
3 4 1


Output


YES
0.5 0.5 1.5 -0.5


Input


2 1
1 2 1


Output


YES
0.3 0.7

Input


3 2
1 2 2
2 3 2


Output


YES
0 2 0


Input


3 4
1 2 2
2 2 1
2 1 1
1 2 2


Output


NO

Note

Note that in the second example the solution is not unique.

Solution (in JAVA):

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

import static java.lang.Math.*;
import static java.util.Arrays.*;

public class cf1387a_2 {

    static int[] par;
    static boolean[] set;

    static int find(int i) {
        return i == par[i] ? i : (par[i] = find(par[i]));
    }

    static void union(int i, int j) {
        int a = find(i), b = find(j);
        if (a != b) {
            par[b] = a;
            set[a] |= set[b];
        }
    }

    public static void main(String[] args) throws IOException {
        int n = rni(), m = ni();
        par = new int[n];
        set = new boolean[n];
        for (int i = 0; i < n; ++i) {
            par[i] = i;
        }
        List<Map<Integer, Integer>> g = new ArrayList<>();
        double[] a = new double[n], b = new double[n];
        fill(a, -2);
        for (int i = 0; i < n; ++i) {
            g.add(new HashMap<>());
        }
        boolean invalid = false;
        for (int i = 0; i < m; ++i) {
            int aa = rni() - 1, bb = ni() - 1, c = ni();
            if (g.get(aa).containsKey(bb) && g.get(aa).get(bb) != c) {
                invalid = true;
            }
            union(aa, bb);
            g.get(aa).put(bb, c);
            g.get(bb).put(aa, c);
            if (aa == bb) {
                a[aa] = 0;
                b[aa] = (double) c / 2;
                set[find(aa)] = true;
            }
        }
        if (invalid) {
            prN();
            close();
            return;
        }
        List<List<Integer>> comps = new ArrayList<>();
        int ind = 0, map[] = new int[n];
        for (int i = 0; i < n; ++i) {
            if (i == par[i]) {
                map[i] = ind++;
                comps.add(new ArrayList<>());
            }
        }
        for (int i = 0; i < n; ++i) {
            comps.get(map[find(i)]).add(i);
        }
        boolean[] vis = new boolean[n];
        for (int i = 0; i < ind; ++i) {
            if (set[find(comps.get(i).get(0))]) {
                for (int j = 0, end = comps.get(i).size(); j < end; ++j) {
                    if (a[comps.get(i).get(j)] == 0) {
                        a[comps.get(i).get(j)] = 1;
                        if (!dfs(g, comps.get(i).get(j), a, b, vis, comps, map)) {
                            prN();
                            close();
                            return;
                        }
                        break;
                    }
                }
            } else {
                a[comps.get(i).get(0)] = 1;
                if (!dfs(g, comps.get(i).get(0), a, b, vis, comps, map)) {
                    prN();
                    close();
                    return;
                }
                if (a[comps.get(i).get(0)] != 0) {
                    // minimize
                    // h();
                    List<Double> median = new ArrayList<>();
                    for (int j = 0, end = comps.get(i).size(); j < end; ++j) {
                        median.add(-a[comps.get(i).get(j)] * b[comps.get(i).get(j)]);
                    }
                    median.sort(Double::compareTo);
                    double x = median.size() % 2 == 0 ? (median.get(median.size() / 2 - 1) + median.get(median.size() / 2)) / 2 : median.get(median.size() / 2);
                    // prln(a);
                    // prln(b);
                    // prln(x);
                    for (int j = 0, end = comps.get(i).size(); j < end; ++j) {
                        b[comps.get(i).get(j)] += a[comps.get(i).get(j)] * x;
                    }
                }
            }
        }
        prY();
        prln(b);
        close();
    }

    static boolean dfs(List<Map<Integer, Integer>> g, int i, double[] a, double[] b, boolean[] vis, List<List<Integer>> comps, int[] map) {
        // prln(i, a[i], b[i]);
        vis[i] = true;
        for (int k : g.get(i).keySet()) {
            double a_prime = -a[i], b_prime = g.get(i).get(k) - b[i];
            // pr("\t");
            // prln(i, k, b_prime);
            if (vis[k]) {
                if (abs(a_prime - a[k]) < 1e-6) {
                    if (abs(b_prime - b[k]) > 1e-6) {
                        return false;
                    }
                } else {
                    // h();
                    double x = (b[k] - b_prime) / (a_prime - a[k]);
                    for (int j : comps.get(map[find(i)])) {
                        if (vis[j]) {
                            b[j] += a[j] * x;
                            a[j] = 0;
                        }
                    }
                }
            } else {
                a[k] = a_prime;
                b[k] = b_prime;
                if (!dfs(g, k, a, b, vis, comps, map)) {
                    return false;
                }
            }
        }
        return true;
    }

    static BufferedReader __in = new BufferedReader(new InputStreamReader(System.in));
    static PrintWriter __out = new PrintWriter(new OutputStreamWriter(System.out));
    static StringTokenizer input;
    static Random __rand = new Random();

    // references
    // IBIG = 1e9 + 7
    // IMAX ~= 2e9
    // LMAX ~= 9e18

    // constants
    static final int IBIG = 1000000007;
    static final int IMAX = 2147483647;
    static final int IMIN = -2147483648;
    static final long LMAX = 9223372036854775807L;
    static final long LMIN = -9223372036854775808L;
    // math util
    static int minof(int a, int b, int c) {return min(a, min(b, c));}
    static int minof(int... x) {if (x.length == 1) return x[0]; if (x.length == 2) return min(x[0], x[1]); if (x.length == 3) return min(x[0], min(x[1], x[2])); int min = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i]; return min;}
    static long minof(long a, long b, long c) {return min(a, min(b, c));}
    static long minof(long... x) {if (x.length == 1) return x[0]; if (x.length == 2) return min(x[0], x[1]); if (x.length == 3) return min(x[0], min(x[1], x[2])); long min = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i]; return min;}
    static int maxof(int a, int b, int c) {return max(a, max(b, c));}
    static int maxof(int... x) {if (x.length == 1) return x[0]; if (x.length == 2) return max(x[0], x[1]); if (x.length == 3) return max(x[0], max(x[1], x[2])); int max = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] > max) max = x[i]; return max;}
    static long maxof(long a, long b, long c) {return max(a, max(b, c));}
    static long maxof(long... x) {if (x.length == 1) return x[0]; if (x.length == 2) return max(x[0], x[1]); if (x.length == 3) return max(x[0], max(x[1], x[2])); long max = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] > max) max = x[i]; return max;}
    static int powi(int a, int b) {if (a == 0) return 0; int ans = 1; while (b > 0) {if ((b & 1) > 0) ans *= a; a *= a; b >>= 1;} return ans;}
    static long powl(long a, int b) {if (a == 0) return 0; long ans = 1; while (b > 0) {if ((b & 1) > 0) ans *= a; a *= a; b >>= 1;} return ans;}
    static int fli(double d) {return (int) d;}
    static int cei(double d) {return (int) ceil(d);}
    static long fll(double d) {return (long) d;}
    static long cel(double d) {return (long) ceil(d);}
    static int gcf(int a, int b) {return b == 0 ? a : gcf(b, a % b);}
    static long gcf(long a, long b) {return b == 0 ? a : gcf(b, a % b);}
    static int lcm(int a, int b) {return a * b / gcf(a, b);}
    static long lcm(long a, long b) {return a * b / gcf(a, b);}
    static int randInt(int min, int max) {return __rand.nextInt(max - min + 1) + min;}
    static long mix(long x) {x += 0x9e3779b97f4a7c15L; x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9L; x = (x ^ (x >> 27)) * 0x94d049bb133111ebL; return x ^ (x >> 31);}
    // array util
    static void reverse(int[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {int swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void reverse(long[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {long swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void reverse(double[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {double swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void reverse(char[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {char swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void shuffle(int[] a) {int n = a.length - 1; for (int i = 0; i < n; ++i) {int ind = randInt(i, n); int swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
    static void shuffle(long[] a) {int n = a.length - 1; for (int i = 0; i < n; ++i) {int ind = randInt(i, n); long swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
    static void shuffle(double[] a) {int n = a.length - 1; for (int i = 0; i < n; ++i) {int ind = randInt(i, n); double swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
    static void rsort(int[] a) {shuffle(a); sort(a);}
    static void rsort(long[] a) {shuffle(a); sort(a);}
    static void rsort(double[] a) {shuffle(a); sort(a);}
    static int[] copy(int[] a) {int[] ans = new int[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    static long[] copy(long[] a) {long[] ans = new long[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    static double[] copy(double[] a) {double[] ans = new double[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    static char[] copy(char[] a) {char[] ans = new char[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    // graph util
    static List<List<Integer>> g(int n) {List<List<Integer>> g = new ArrayList<>(); for (int i = 0; i < n; ++i) g.add(new ArrayList<>()); return g;}
    static List<Set<Integer>> sg(int n) {List<Set<Integer>> g = new ArrayList<>(); for (int i = 0; i < n; ++i) g.add(new HashSet<>()); return g;}
    static void c(List<? extends Collection<Integer>> g, int u, int v) {g.get(u).add(v); g.get(v).add(u);}
    static void cto(List<? extends Collection<Integer>> g, int u, int v) {g.get(u).add(v);}
    static void dc(List<? extends Collection<Integer>> g, int u, int v) {g.get(u).remove(v); g.get(v).remove(u);}
    static void dcto(List<? extends Collection<Integer>> g, int u, int v) {g.get(u).remove(v);}
    // input
    static void r() throws IOException {input = new StringTokenizer(rline());}
    static int ri() throws IOException {return Integer.parseInt(rline());}
    static long rl() throws IOException {return Long.parseLong(rline());}
    static double rd() throws IOException {return Double.parseDouble(rline());}
    static int[] ria(int n) throws IOException {int[] a = new int[n]; r(); for (int i = 0; i < n; ++i) a[i] = ni(); return a;}
    static int[] riam1(int n) throws IOException {int[] a = new int[n]; r(); for (int i = 0; i < n; ++i) a[i] = ni() - 1; return a;}
    static long[] rla(int n) throws IOException {long[] a = new long[n]; r(); for (int i = 0; i < n; ++i) a[i] = nl(); return a;}
    static double[] rda(int n) throws IOException {double[] a = new double[n]; r(); for (int i = 0; i < n; ++i) a[i] = nd(); return a;}
    static char[] rcha() throws IOException {return rline().toCharArray();}
    static String rline() throws IOException {return __in.readLine();}
    static String n() {return input.nextToken();}
    static int rni() throws IOException {r(); return ni();}
    static int ni() {return Integer.parseInt(n());}
    static long rnl() throws IOException {r(); return nl();}
    static long nl() {return Long.parseLong(n());}
    static double rnd() throws IOException {r(); return nd();}
    static double nd() {return Double.parseDouble(n());}
    static List<List<Integer>> rg(int n, int m) throws IOException {List<List<Integer>> g = g(n); for (int i = 0; i < m; ++i) c(g, rni() - 1, ni() - 1); return g;}
    static void rg(List<List<Integer>> g, int m) throws IOException {for (int i = 0; i < m; ++i) c(g, rni() - 1, ni() - 1);}
    static List<List<Integer>> rdg(int n, int m) throws IOException {List<List<Integer>> g = g(n); for (int i = 0; i < m; ++i) cto(g, rni() - 1, ni() - 1); return g;}
    static void rdg(List<List<Integer>> g, int m) throws IOException {for (int i = 0; i < m; ++i) cto(g, rni() - 1, ni() - 1);}
    static List<Set<Integer>> rsg(int n, int m) throws IOException {List<Set<Integer>> g = sg(n); for (int i = 0; i < m; ++i) c(g, rni() - 1, ni() - 1); return g;}
    static void rsg(List<Set<Integer>> g, int m) throws IOException {for (int i = 0; i < m; ++i) c(g, rni() - 1, ni() - 1);}
    static List<Set<Integer>> rdsg(int n, int m) throws IOException {List<Set<Integer>> g = sg(n); for (int i = 0; i < m; ++i) cto(g, rni() - 1, ni() - 1); return g;}
    static void rdsg(List<Set<Integer>> g, int m) throws IOException {for (int i = 0; i < m; ++i) cto(g, rni() - 1, ni() - 1);}
    // output
    static void pr(int i) {__out.print(i);}
    static void prln(int i) {__out.println(i);}
    static void pr(long l) {__out.print(l);}
    static void prln(long l) {__out.println(l);}
    static void pr(double d) {__out.print(d);}
    static void prln(double d) {__out.println(d);}
    static void pr(char c) {__out.print(c);}
    static void prln(char c) {__out.println(c);}
    static void pr(char[] s) {__out.print(new String(s));}
    static void prln(char[] s) {__out.println(new String(s));}
    static void pr(String s) {__out.print(s);}
    static void prln(String s) {__out.println(s);}
    static void pr(Object o) {__out.print(o);}
    static void prln(Object o) {__out.println(o);}
    static void prln() {__out.println();}
    static void pryes() {prln("yes");}
    static void pry() {prln("Yes");}
    static void prY() {prln("YES");}
    static void prno() {prln("no");}
    static void prn() {prln("No");}
    static void prN() {prln("NO");}
    static void pryesno(boolean b) {prln(b ? "yes" : "no");};
    static void pryn(boolean b) {prln(b ? "Yes" : "No");}
    static void prYN(boolean b) {prln(b ? "YES" : "NO");}
    static void prln(int... a) {for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i); if (a.length > 0) prln(a[a.length - 1]); else prln();}
    static void prln(long... a) {for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i); if (a.length > 0) prln(a[a.length - 1]); else prln();}
    static void prln(double... a) {for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i); if (a.length > 0) prln(a[a.length - 1]); else prln();}
    static <T> void prln(Collection<T> c) {int n = c.size() - 1; Iterator<T> iter = c.iterator(); for (int i = 0; i < n; pr(iter.next()), pr(' '), ++i); if (n >= 0) prln(iter.next()); else prln();}
    static void h() {prln("hlfd"); flush();}
    static void flush() {__out.flush();}
    static void close() {__out.close();}}