Problem: A society can be represented by a connected, undirected graph of n vertices and m edges. The vertices represent people, and an edge (i,j) represents a friendship between people i and j.

In society, the i-th person has an income a_i. A person i is envious of person j if a_j=a_i+1. That is if person j has exactly 1 more unit of income than person i.

The society is called capitalist if for every pair of friends one is envious of the other. For some friendships, you know which friend is envious of the other. For the remaining friendships, you do not know the direction of envy.

The income inequality of society is defined as max_{1 ≤ i ≤ n} a_i - min_{1 ≤ i ≤ n} a_i.

You only know the friendships and not the incomes. If it is impossible for this society to be capitalist with the given knowledge, you should report about it. Otherwise, you should find an assignment of incomes in which the society is capitalist, and the income inequality is maximized.

Input

The first line contains two integers n, m (1≤ n≤ 200, n-1≤ m≤ 2000) — the number of people and friendships, respectively.

The following m lines describe the friendships. Each friendship is described by three integers i, j, b (1≤ i, j≤ n, i≠ j, 0≤ b≤ 1). This denotes that people i and j are friends. If b=1, we require that person i is envious of person j. If b=0, one friend should be envious of the other in either direction.

There is at most one friendship between each pair of people. It is guaranteed that if we consider the friendships as undirected edges, the graph is connected.

Output

Print "YES" if it is possible that the society is capitalist, or "NO" otherwise. You can print characters in any case (upper or lower).

If the answer is "YES", you should print two additional lines. In the first line, print the maximum possible income inequality. On the next line you should print n integers a_1,…, a_n (0≤ a_i≤ 10^6), where a_i denotes the income of the i-th person.

We can prove that if there exists a solution, there exists one where 0≤ a_i≤ 10^6 for all i.

If there exist multiple solutions, print any.

Examples

Input


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


Output


YES
3
3 2 1 3 1 0 


Input


4 4
1 2 1
2 3 0
3 4 1
4 1 1


Output


NO


Input


1 0


Output


YES
0
0 

Note

In the first test, we can show that an income inequality greater than 3 is impossible for the given society. In the given answer with income inequality equal to 3:

  * Person 2 is envious of person 1. 
  * Person 3 is envious of person 2. 
  * Person 5 is envious of person 2. 
  * Person 6 is envious of person 5 (the required direction is satisfied). 
  * Person 6 is envious of person 3. 
  * Person 2 is envious of person 4 (the required direction is satisfied). 



In the second test, we can show that there is no way to assign incomes to satisfy all requirements.

Solution (in CPP):

Solution:
/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author Egor Kulikov
 */

// Actual solution is at the bottom





#include <bits/stdc++.h>

using namespace std;

#define all(v) (v).begin(), (v).end()

using ll = long long;
using ull = unsigned long long;
using li = __int128;
using uli = unsigned __int128;
using ld = long double;
using pii = pair<int, int>;
using vi = vector<int>;

void doReplace() {
}

template <typename T, typename U, typename...Vs>
void doReplace(T& t, const U& u, Vs&& ...vs) {
    t = u;
    doReplace(vs...);
}

template <typename T, typename...Us>
T minim(T& was, const T& cand, Us&& ...us) {
    if (was > cand) {
        was = cand;
        doReplace(us...);
    }
    return was;
}

template <typename T, typename...Us>
T maxim(T& was, const T& cand, Us&& ...us) {
    if (was < cand) {
        was = cand;
        doReplace(us...);
    }
    return was;
}


template <typename D>
D dPower(D base, ll exponent) {
    if (exponent < 0) {
        return dPower(1 / base, -exponent);
    }
    if (exponent == 0) {
        return 1;
    }
    if ((exponent & 1) == 1) {
        return dPower(base, exponent - 1) * base;
    } else {
        D res = dPower(base, exponent >> 1);
        return res * res;
    }
}


class NumberIterator : iterator<forward_iterator_tag, int> {
public:
    int v;

    NumberIterator(int v) : v(v) {}

    operator int&() { return v; }

    int operator*() { return v; }
};

class range : pii {
public:
    range(int begin, int end) : pii(begin, max(begin, end)) {}

    range(int n) : pii(0, max(0, n)) {}

    NumberIterator begin() {
        return first;
    }

    NumberIterator end() {
        return second;
    }
};


template <typename T>
class NeedFill {
    struct Fallback {
        int begin;
    }; // add member name "find"
    struct Derived : T, Fallback {
    };

    template <typename U, U>
    struct Check;

    typedef char Yes[1];  // typedef for an array of size one.
    typedef char No[2];  // typedef for an array of size two.

    template <typename U>
    static No& func(Check<int Fallback::*, &U::begin>*);

    template <typename U>
    static Yes& func(...);

public:
    typedef NeedFill type;
    enum {
        value = sizeof(func<Derived>(0)) == sizeof(Yes)
    };
};

template <>
class NeedFill<int> {
public:
    const static bool value = false;
};

template <>
class NeedFill<unsigned> {
public:
    const static bool value = false;
};

template <>
class NeedFill<bool> {
public:
    const static bool value = true;
};

template <>
class NeedFill<ll> {
public:
    const static bool value = false;
};

template <>
class NeedFill<double> {
public:
    const static bool value = false;
};

template <>
class NeedFill<ld> {
public:
    const static bool value = false;
};

template <>
class NeedFill<char> {
public:
    const static bool value = false;
};

template <typename T>
class arr {
    T* b;
    int n;

    void allocate(int sz) {
#ifdef LOCAL
        if (sz < 0) {
            throw "bad alloc";
        }
#endif
        n = sz;
        if (sz > 0) {
            b = (T*) (::operator new(sz * sizeof(T)));
        } else {
            b = nullptr;
        }
    }

public:
    arr(int n = 0) {
        allocate(n);
        if (NeedFill<T>::value) {
            for (int i : range(n)) {
                ::new((void*) (b + i)) T;
            }
        }
#ifdef LOCAL
        view();
#endif
    }

    arr(int n, const T& init) {
        allocate(n);
        for (int i : range(n)) {
            ::new((void*) (b + i)) T(init);
        }
#ifdef LOCAL
        view();
#endif
    }

    arr(T* b, int n) : arr(b, b + n) {}

    arr(T* b, T* e) : b(b), n(e - b) {}

    arr(initializer_list<T> l) : arr(l.size()) {
        if (n > 0) {
            memcpy(b, l.begin(), n * sizeof(T));
        }
    }

    int size() const {
        return n;
    }

    T* begin() {
        return b;
    }

    const T* begin() const {
        return b;
    }

    T* end() {
        return b + n;
    }

    const T* end() const {
        return b + n;
    }

    arr<T> clone() const {
        arr<T> res(n);
        copy(b, b + n, res.begin());
        return res;
    }

    T& operator[](int at) {
#ifdef LOCAL
        if (at < 0 || at >= n) {
            throw "Out of bounds";
        }
#endif
        return b[at];
    }

    const T& operator[](int at) const {
#ifdef LOCAL
        if (at < 0 || at >= n) {
            throw "Out of bounds";
        }
#endif
        return b[at];
    }

    bool operator==(const arr& other) const {
        if (n != other.n) {
            return false;
        }
        for (int i : range(n)) {
            if (b[i] != other.b[i]) {
                return false;
            }
        }
        return true;
    }

    vector<T> view() {
        return vector<T>(b, b + n);
    }
};

typedef arr<int> arri;

void decreaseByOne() {}

template <typename T, class...Vs>
void decreaseByOne(arr<T>& array, Vs& ...vs) {
    int n = array.size();
    for (int i : range(n)) {
        array[i]--;
    }
    decreaseByOne(vs...);
}


template <typename T>
class arr2d {
    T* b;
    int d1;
    int d2;
    int sz;

    void allocate(int n) {
#ifdef LOCAL
        if (n < 0) {
            throw "bad alloc";
        }
#endif
        if (n > 0) {
            b = (T*) (::operator new(n * sizeof(T)));
        } else {
            b = nullptr;
        }
    }

public:
    arr2d(int d1 = 0, int d2 = 0) : d1(d1), d2(d2), sz(d1 * d2) {
#ifdef LOCAL
        if (d1 < 0 || d2 < 0) {
            throw "bad alloc";
        }
#endif
        allocate(sz);
        if (NeedFill<T>::value) {
            for (int i : range(sz)) {
                ::new((void*) (b + i)) T;
            }
        }
#ifdef LOCAL
        view();
#endif
    }

    arr2d(int d1, int d2, const T& init) : d1(d1), d2(d2), sz(d1 * d2) {
#ifdef LOCAL
        if (d1 < 0 || d2 < 0) {
            throw "bad alloc";
        }
#endif
        allocate(sz);
        for (int i : range(sz)) {
            ::new((void*) (b + i)) T(init);
        }
#ifdef LOCAL
        view();
#endif
    }

    arr2d(T* b, int d1, int d2) : b(b), d1(d1), d2(d2), sz(d1 * d2) {}

    int size() const {
        return sz;
    }

    int dim1() const {
        return d1;
    }

    int dim2() const {
        return d2;
    }

    T* begin() {
        return b;
    }

    T* end() {
        return b + sz;
    }

    T& operator()(int i1, int i2) {
#ifdef LOCAL
        if (i1 < 0 || i1 >= d1 || i2 < 0 || i2 >= d2) {
            throw "Out of bounds";
        }
#endif
        return b[i1 * d2 + i2];
    }

    const T& operator()(int i1, int i2) const {
#ifdef LOCAL
        if (i1 < 0 || i1 >= d1 || i2 < 0 || i2 >= d2) {
            throw "Out of bounds";
        }
#endif
        return b[i1 * d2 + i2];
    }

    T& operator[](const pii& p) {
        return operator()(p.first, p.second);
    }

    const T& operator[](const pii& p) const {
        return operator()(p.first, p.second);
    }

    arr<T> operator[](int at) {
#ifdef LOCAL
        if (at < 0 || at >= d1) {
            throw "Out of bounds";
        }
#endif
        return arr<T>(b + at * d2, d2);
    }

    vector<vector<T>> view() {
        vector<vector<T>> res(min(d1, 50));
        for (int i : range(res.size())) {
            res[i] = (*this)[i].view();
        }
        return res;
    }

};


inline bool isWhitespace(int c) {
    return isspace(c) || c == EOF;
}

class Input {
private:
    bool exhausted = false;
    int bufSize = 4096;
    char* buf = new char[bufSize];
    int bufRead = 0;
    int bufAt = 0;

public:
    inline int get() {
        if (exhausted) {
#ifdef LOCAL
            throw "Input exhausted";
#endif
            return EOF;
        }
        if (bufRead == bufAt) {
            bufRead = fread(buf, sizeof(char), bufSize, stdin);
            bufAt = 0;
        }
        if (bufRead == bufAt) {
            exhausted = true;
            return EOF;
        }
        return buf[bufAt++];
    }

    inline int peek() {
        if (exhausted) {
            return EOF;
        }
        if (bufRead == bufAt) {
            bufRead = fread(buf, sizeof(char), bufSize, stdin);
            bufAt = 0;
        }
        if (bufRead == bufAt) {
            exhausted = true;
            getchar();
            return EOF;
        }
        return buf[bufAt];
    }

private:
    template <typename T>
    inline T readInteger() {
        int c = skipWhitespace();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = get();
        }
        T res = 0;
        do {
            if (!isdigit(c)) {
#ifdef LOCAL
                throw "Number format error";
#endif
                return sgn * res;
            }
            res *= 10;
            res += c - '0';
            c = get();
        } while (!isWhitespace(c));
        return res * sgn;
    }

    void initArrays(int) {}

    template <typename T, class...Vs>
    void initArrays(int n, arr<T>& array, Vs& ...vs) {
        array = arr<T>(n);
        initArrays(n, vs...);
    }

    template <typename T, class...Vs>
    void initArrays(int n, vector<T>&, Vs& ...vs) {
        initArrays(n, vs...);
    }

    void readImpl(int) {}

    template <typename T, class...Vs>
    void readImpl(int i, arr<T>& arr, Vs& ...vs) {
        arr[i] = readType<T>();
        readImpl(i, vs...);
    }

    template <typename T, class...Vs>
    void readImpl(int i, vector<T>& arr, Vs& ...vs) {
        arr.push_back(readType<T>());
        readImpl(i, vs...);
    }

public:
    inline int skipWhitespace() {
        int c;
        while (isWhitespace(c = get()) && c != EOF);
        return c;
    }

    inline int peekNext() {
        while (isWhitespace(peek()) && peek() != EOF) {
            get();
        }
        return peek();
    }

    inline int readInt() {
        return readInteger<int>();
    }

    inline ll readLong() {
        return readInteger<ll>();
    }

    inline unsigned readUnsigned() {
        return readInteger<unsigned>();
    }

    string readString() {
        int c = skipWhitespace();
        if (c == EOF) {
#ifdef LOCAL
            throw "Input exhausted";
#endif
            return "";
        }
        string res;
        do {
            res.push_back(c);
        } while (!isWhitespace(c = get()));
        return res;
    }

    arri readIntArray(int size) {
        return readArray<int>(size);
    }

    arr<ll> readLongArray(int size) {
        return readArray<ll>(size);
    }

    arr<double> readDoubleArray(int size) {
        return readArray<double>(size);
    }

    arr<string> readStringArray(int size) {
        return readArray<string>(size);
    }

    arr<char> readCharArray(int size) {
        return readArray<char>(size);
    }

    template <typename T>
    T readType() {
        throw "Operation not supported";
    }

    template <typename U, typename V>
    pair<U, V> readType() {
        U first = readType<U>();
        V second = readType<V>();
        return make_pair(first, second);
    }

    template <typename T>
    arr<T> readArray(int n) {
        arr<T> res(n, T());
        for (int i : range(n)) {
            res[i] = readType<T>();
        }
        return res;
    }


    template <class...Vs>
    void readArrays(int n, Vs& ...vs) {
        initArrays(n, vs...);
        for (int i : range(n)) {
            readImpl(i, vs...);
        }
    }

    template <typename U, typename V>
    arr<pair<U, V>> readArray(int n) {
        arr<pair<U, V>> res(n);
        for (int i : range(n)) {
            res[i] = readType<U, V>();
        }
        return res;
    }

    template <typename T>
    arr2d<T> readTable(int rows, int cols) {
        arr2d<T> result(rows, cols);
        for (int i : range(rows)) {
            for (int j : range(cols)) {
                result(i, j) = readType<T>();
            }
        }
        return result;
    }

    arr2d<int> readIntTable(int rows, int cols) {
        return readTable<int>(rows, cols);
    }

    arr2d<char> readCharTable(int rows, int cols) {
        return readTable<char>(rows, cols);
    }

    string readLine() {
        int c = get();
        if (c == EOF) {
#ifdef LOCAL
            throw "Input exhausted";
#endif
            return "";
        }
        string res;
        while (c != '\n' && c != '\r' && c != EOF) {
            res.push_back(c);
            c = get();
        }
        if (c == '\r' && peek() == '\n') {
            get();
        }
        return res;
    }

    inline double readDouble() {
        int c = skipWhitespace();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = get();
        }
        double res = 0;
        do {
            if (tolower(c) == 'e') {
                return sgn * res * dPower(double(10), readInt());
            }
            if (!isdigit(c)) {
#ifdef LOCAL
                throw "Number format error";
#endif
                return sgn * res;
            }
            res *= 10;
            res += c - '0';
            c = get();
        } while (!isWhitespace(c) && c != '.');
        if (c == '.') {
            double add = 0;
            int length = 0;
            c = get();
            do {
                if (tolower(c) == 'e') {
                    return sgn * (res + add * dPower(double(10), -length)) * dPower(double(10), readInt());
                }
                if (!isdigit(c)) {
#ifdef LOCAL
                    throw "Number format error";
#endif
                    res += add * dPower(10, -length);
                    return res * sgn;
                }
                add *= 10;
                add += c - '0';
                length++;
                c = get();
            } while (!isWhitespace(c));
            res += add * dPower(double(10), -length);
        }
        return res * sgn;
    }

    inline char readChar() {
        int c = skipWhitespace();
        if (c == EOF) {
#ifdef LOCAL
            throw "Input exhausted";
#endif
            return 0;
        }
        return c;
    }

    inline bool isExhausted() { return exhausted; }

    inline void setBufSize(int newBufSize) {
        if (newBufSize > bufSize) {
            char* newBuf = new char[newBufSize];
            memcpy(newBuf, buf, bufSize);
            buf = newBuf;
        }
        bufSize = newBufSize;
    }
};

template <>
inline double Input::readType() {
    return readDouble();
}

template <>
inline int Input::readType() {
    return readInt();
}

template <>
inline ll Input::readType() {
    return readLong();
}

template <>
inline unsigned Input::readType() {
    return readUnsigned();
}

template <>
inline char Input::readType() {
    return readChar();
}

template <>
inline string Input::readType() {
    return readString();
}

Input in;


class Output {
private:
    ostream* out;

    template <typename T>
    inline void printSingle(const T& value) {
        *out << value;
    }

    template <typename T>
    void printSingle(const vector<T>& array) {
        size_t n = array.size();
        for (int i : range(n)) {
            *out << array[i];
            if (i + 1 != n) {
                *out << ' ';
            }
        }
    }

    template <typename T>
    void printSingle(const arr<T>& array) {
        int n = array.size();
        for (int i : range(n)) {
            *out << array[i];
            if (i + 1 != n) {
                *out << ' ';
            }
        }
    }

    template <typename T>
    void printSingle(const arr2d<T>& array) {
        size_t n = array.dim1();
        size_t m = array.dim2();
        for (int i : range(n)) {
            for (int j : range(m)) {
                *out << array(i, j);
                if (j + 1 != m) {
                    *out << ' ';
                }
            }
            if (i + 1 != n) {
                *out << '\n';
            }
        }
    }

    template <typename T, typename U>
    inline void printSingle(const pair<T, U>& value) {
        *out << value.first << ' ' << value.second;
    }

public:
    bool autoflush;

    Output(ostream& out, bool autoflush) : out(&out), autoflush(autoflush) {
        setPrecision(20);
    }

    void setOut(ostream& nOut) {
        out = &nOut;
        setPrecision(20);
    }

    inline void print() {}

    template <typename T, typename...Targs>
    inline void print(const T& first, const Targs... args) {
        printSingle(first);
        if (sizeof...(args) != 0) {
            *out << ' ';
            print(args...);
        }
        if (autoflush) {
            flush();
        }
    }

    template <typename...Targs>
    inline void printLine(const Targs... args) {
        print(args...);
        *out << '\n';
        if (autoflush) {
            flush();
        }
    }

    inline void flush() {
        out->flush();
    }

    inline void setPrecision(int digs) {
        *out << fixed << setprecision(digs);
    }
};

Output out(cout, false);
Output err(cerr, true);

#ifdef LOCAL
#define debug(x) err.printLine(#x, '=', x);
#else
#define debug(x)
#endif


template <typename T>
inline void unique(vector<T>& v) {
    v.resize(unique(all(v)) - v.begin());
}

arri createOrder(int n) {
    arri order(n);
    for (int i = 0; i < n; i++) {
        order[i] = i;
    }
    return order;
}

arri inverse(const arri& p) {
    arri res(p.size());
    for (int i : range(p.size())) {
        res[p[i]] = i;
    }
    return res;
}

template <typename T, typename Iterator>
inline void addAll(vector<T>& v, Iterator begin, Iterator end) {
    v.insert(v.end(), begin, end);
}

template <class Collection, typename Iterator>
inline void addAll(Collection& v, Iterator begin, Iterator end) {
    v.insert(begin, end);
}

template <typename Iterator>
arri getQty(Iterator begin, Iterator end, int length) {
    arri res(length, 0);
    for (Iterator it = begin; it != end; it++) {
        res[*it]++;
    }
    return res;
}

template <typename Iterator>
arri getQty(Iterator begin, Iterator end) {
    return getQty(begin, end, *max_element(begin, end) + 1);
}

template <class Collection>
void collect(Collection&) {}

template <class Collection, class Other, class ...Vs>
void collect(Collection& all, Other& a, Vs& ...vs) {
    addAll(all, all(a));
    collect(all, vs...);
}

void replace(const vi&) {}

template <class ...Vs>
void replace(const vi& all, vi& a, Vs& ...vs) {
    for (int& i : a) {
        i = lower_bound(all(all), i) - all.begin();
    }
    replace(all, vs...);
}

template <class ...Vs>
void replace(const vi& all, arri& a, Vs& ...vs) {
    for (int& i : a) {
        i = lower_bound(all(all), i) - all.begin();
    }
    replace(all, vs...);
}

template <class ...Vs>
vi compress(Vs& ...vs) {
    vi vals;
    collect(vals, vs...);
    sort(all(vals));
    unique(vals);
    replace(vals, vs...);
    return vals;
}


template <class Edge>
class Graph {
public:
    int vertexCount;
    int edgeCount = 0;
private:
    vector<vector<Edge>> edges;

public:
    Graph(int vertexCount) : vertexCount(vertexCount), edges(vertexCount, vector<Edge>()) {}

    template <typename...Ts>
    int addEdge(int from, int to, Ts... args) {
#ifdef LOCAL
        if (from < 0 || to < 0 || from >= vertexCount || to >= vertexCount) {
            throw "Out of bounds";
        }
#endif
        edges[from].emplace_back(to, edgeCount, args...);
        int directId = edges[from].size() - 1;
        if (Edge::reversable) {
            edges[to].push_back(edges[from][directId].reverseEdge(from));
            int revId = edges[to].size() - 1;
            edges[from][directId].setReverseId(revId);
            edges[to][revId].setReverseId(directId);
        }
        edgeCount++;
        return directId;
    }

    vector<Edge>& operator[](int at) {
        return edges[at];
    }

    void addVertices(int count) {
        vertexCount += count;
        edges.resize(vertexCount);
    }

    void clear() {
        edgeCount = 0;
        for (int i : range(vertexCount)) {
            edges[i].clear();
        }
    }
};


class BaseEdge {
public:
    const static bool reversable = false;
    int to;
    int id;

    BaseEdge(int to, int id) : to(to), id(id) {
    }

    BaseEdge reverseEdge(int) {
        throw "Unsupported operation exception";
    }

    void setReverseId(int) {
        throw "Unsupported operation exception";
    }
};


template <typename W>
class WeightedEdge : public BaseEdge {
public:
    const static bool reversable = false;
    W weight;

    WeightedEdge(int to, int id, W weight) : BaseEdge(to, id), weight(weight) {
    }

    WeightedEdge<W> reverseEdge(int) {
        throw "Unsupported operation exception";
    }

    void setReverseId(int) {
        throw "Unsupported operation exception";
    }
};


template <typename T>
class que : public queue<T> {
    using parent = queue<T>;
public:
    que() : parent() {}

    que(const que<T>& q) : parent(q) {}

    que(que<T>&& q) noexcept: parent(move(q)) {}

    T pop() {
#ifdef LOCAL
        if (parent::empty()) {
            throw "Pop on empty queue";
        }
#endif
        T res = parent::front();
        parent::pop();
        return res;
    }

    que<T>& operator=(que<T>&& __x) noexcept {
        parent::operator=(__x);
        return *this;
    }

    que<T>& operator=(const que<T>& __x) {
        parent::operator=(__x);
        return *this;
    }
};

using qi = que<int>;


class EKapitalizm {
public:
    void solve() {
        int n = in.readInt();
        int m = in.readInt();
        arri u, v, b;
        in.readArrays(m, u, v, b);
        decreaseByOne(u, v);

        Graph<WeightedEdge<int>> graph(n);
        for (int i : range(m)) {
            graph.addEdge(u[i], v[i], b[i]);
            graph.addEdge(v[i], u[i], -b[i]);
        }
        arri color(n, 0);
        color[0] = 1;
        que<int> q;
        q.push(0);
        while (!q.empty()) {
            int cur = q.pop();
            for (auto& e : graph[cur]) {
                if (color[e.to] == color[cur]) {
                    out.printLine("NO");
                    return;
                }
                if (color[e.to] == 0) {
                    color[e.to] = -color[cur];
                    q.push(e.to);
                }
            }
        }
        int answer = -1;
        arri delta(n);
        arri lim(n);
        for (int i : range(n)) {
            fill(all(lim), 1000 * n);
            lim[i] = 0;
            bool good = true;
            while (true) {
                bool update = false;
                for (int j : range(m)) {
                    if (b[j] == 0 && abs(lim[u[j]] - lim[v[j]]) > 1) {
                        if (lim[u[j]] < lim[v[j]]) {
                            lim[v[j]] = lim[u[j]] + 1;
                            update = true;
                        } else {
                            lim[u[j]] = lim[v[j]] + 1;
                            update = true;
                        }
                    } else if (b[j] == 1) {
                        if (lim[u[j]] > lim[v[j]] - 1) {
                            lim[u[j]] = lim[v[j]] - 1;
                            update = true;
                        } else if (lim[v[j]] > lim[u[j]] + 1) {
                            lim[v[j]] = lim[u[j]] + 1;
                            update = true;
                        }
                    }
                }
                if (!update) {
                    break;
                }
                for (int j : range(n)) {
                    if (lim[j] < 0) {
                        good = false;
                        break;
                    }
                }
                if (!good) {
                    break;
                }
            }
            if (good && answer < *max_element(all(lim))) {
                answer = *max_element(all(lim));
                copy(all(lim), delta.begin());
            }
        }
        if (answer == -1) {
            out.printLine("NO");
            return;
        }
        out.printLine("YES");
        out.printLine(answer);
        out.printLine(delta);
        /*arri delta(n, 0);
        arr2d<int> rel(n, n, -2);
        for (int i : range(m)) {
            rel(u[i], v[i]) = b[i];
            rel(v[i], u[i]) = -b[i];
        }
        set<vi> sets;
        for (int i : range(n)) {
            sets.insert(vi(1, i));
        }
        while (true) {
            vi f;
            vi e;
            for (auto& s : sets) {
                for (auto& t : sets) {
                    if (s[0] == t[0]) {
                        break;
                    }
                    int minDelta = numeric_limits<int>::min();
                    int maxDelta = numeric_limits<int>::max();
                    int deltaOddity = -1;
                    for (int i : s) {
                        for (int j : t) {
                            if (rel(i, j) == -2) {
                                continue;
                            }
                            if (deltaOddity != -1 && deltaOddity != abs(delta[i] - delta[j]) % 2) {
                                out.printLine("NO");
                                return;
                            }
                            deltaOddity = abs(delta[i] - delta[j]) % 2;
                            if (rel(i, j) == 0) {
                                maxim(minDelta, delta[j] - delta[i] - 1);
                                minim(maxDelta, delta[j] - delta[i] + 1);
                            } else {
                                maxim(minDelta, delta[j] - delta[i] + rel(i, j));
                                minim(maxDelta, delta[j] - delta[i] + rel(i, j));
                            }
                        }
                    }
                    if (minDelta > maxDelta) {
                        out.printLine("NO");
                        return;
                    }
                    if (minDelta == maxDelta) {
                        f = s;
                        e = t;
                        for (int i : t) {
                            delta[i] -= maxDelta;
                        }
                        break;
                    }
                }
                if (!f.empty()) {
                    break;
                }
            }
            if (f.empty()) {
                break;
            }
            sets.erase(f);
            sets.erase(e);
            addAll(f, all(e));
            sets.insert(f);
        }*/

    }
};


int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(0);
#ifdef LOCAL_RELEASE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
    auto time = clock();
#endif
    EKapitalizm solver;


    solver.solve();
    fflush(stdout);
#ifdef LOCAL_RELEASE
    cerr << setprecision(3) << double(clock() - time) / CLOCKS_PER_SEC << endl;
#endif
    return 0;
}