You are given a connected undirected graph consisting of n vertices and m edges. There are no self-loops or multiple edges in the given graph.

You have to direct its edges in such a way that the obtained directed graph does not contain any paths of length two or greater (where the length of path is denoted as the number of traversed edges).

Input

The first line contains two integer numbers n and m (2 ≤ n ≤ 2 ⋅ 10^5, n - 1 ≤ m ≤ 2 ⋅ 10^5) — the number of vertices and edges, respectively.

The following m lines contain edges: edge i is given as a pair of vertices u_i, v_i (1 ≤ u_i, v_i ≤ n, u_i ≠ v_i). There are no multiple edges in the given graph, i. e. for each pair (u_i, v_i) there are no other pairs (u_i, v_i) and (v_i, u_i) in the list of edges. It is also guaranteed that the given graph is connected (there is a path between any pair of vertex in the given graph).

Output

If it is impossible to direct edges of the given graph in such a way that the obtained directed graph does not contain paths of length at least two, print "NO" in the first line.

Otherwise print "YES" in the first line, and then print any suitable orientation of edges: a binary string (the string consisting only of '0' and '1') of length m. The i-th element of this string should be '0' if the i-th edge of the graph should be directed from u_i to v_i, and '1' otherwise. Edges are numbered in the order they are given in the input.

Example

Input


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


Output


YES
10100

Note

The picture corresponding to the first example: <image>

And one of possible answers: <image>
#pragma GCC optimize("Ofast")  
#pragma GCC target("avx,avx2,fma") 
#include <bits/stdc++.h>
using namespace std;
 
#define ll long long
#define ld long double
#define ar array
 
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
 
template <typename T> using oset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
 
#define vt vector
#define pb push_back
#define all(c) (c).begin(), (c).end()
#define sz(x) (int)(x).size()
 
#define F_OR(i, a, b, s) for (int i=(a); (s)>0?i<(b):i>(b); i+=(s))
#define F_OR1(e) F_OR(i, 0, e, 1)
#define F_OR2(i, e) F_OR(i, 0, e, 1)
#define F_OR3(i, b, e) F_OR(i, b, e, 1)
#define F_OR4(i, b, e, s) F_OR(i, b, e, s)
#define GET5(a, b, c, d, e, ...) e
#define F_ORC(...) GET5(__VA_ARGS__, F_OR4, F_OR3, F_OR2, F_OR1)
#define FOR(...) F_ORC(__VA_ARGS__)(__VA_ARGS__)
#define EACH(x, a) for (auto& x: a)
 
template<class T> bool umin(T& a, const T& b) {
    return b<a?a=b, 1:0;
}
template<class T> bool umax(T& a, const T& b) { 
    return a<b?a=b, 1:0;
} 
 
ll FIRSTTRUE(function<bool(ll)> f, ll lb, ll rb) {
    while(lb<rb) {
        ll mb=(lb+rb)/2;
        f(mb)?rb=mb:lb=mb+1; 
    } 
    return lb;
}
ll LASTTRUE(function<bool(ll)> f, ll lb, ll rb) {
    while(lb<rb) {
        ll mb=(lb+rb+1)/2;
        f(mb)?lb=mb:rb=mb-1; 
    } 
    return lb;
}
 
template<class A> void read(vt<A>& v);
template<class A, size_t S> void read(ar<A, S>& a);
template<class T> void read(T& x) {
    cin >> x;
}
void read(double& d) {
    string t;
    read(t);
    d=stod(t);
}
void read(long double& d) {
    string t;
    read(t);
    d=stold(t);
}
template<class H, class... T> void read(H& h, T&... t) {
    read(h);
    read(t...);
}
template<class A> void read(vt<A>& x) {
    EACH(a, x)
        read(a);
}
template<class A, size_t S> void read(array<A, S>& x) {
    EACH(a, x)
        read(a);
}
 
string to_string(char c) {
    return string(1, c);
}
string to_string(bool b) {
    return b?"true":"false";
}
string to_string(const char* s) {
    return string(s);
}
string to_string(string s) {
    return s;
}
string to_string(vt<bool> v) {
    string res;
    FOR(sz(v))
        res+=char('0'+v[i]);
    return res;
}
 
template<size_t S> string to_string(bitset<S> b) {
    string res;
    FOR(S)
        res+=char('0'+b[i]);
    return res;
}
template<class T> string to_string(T v) {
    bool f=1;
    string res;
    EACH(x, v) {
        if(!f)
            res+=' ';
        f=0;
        res+=to_string(x);
    }
    return res;
}
 
template<class A> void write(A x) {
    cout << to_string(x);
}
template<class H, class... T> void write(const H& h, const T&... t) { 
    write(h);
    write(t...);
}
void print() {
    write("\n");
}
template<class H, class... T> void print(const H& h, const T&... t) { 
    write(h);
    if(sizeof...(t))
        write(' ');
    print(t...);
}
 
void DBG() {
    cerr << "]" << endl;
}
template<class H, class... T> void DBG(H h, T... t) {
    cerr << to_string(h);
    if(sizeof...(t))
        cerr << ", ";
    DBG(t...);
}
#ifdef _DEBUG
#define dbg(...) cerr << "LINE(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#else
#define dbg(...) 0
#endif
 
template<class T> void offset(ll o, T& x) {
    x+=o;
}
template<class T> void offset(ll o, vt<T>& x) {
    EACH(a, x)
        offset(o, a);
}
template<class T, size_t S> void offset(ll o, ar<T, S>& x) {
    EACH(a, x)
        offset(o, a);
}
 
mt19937 mt_rng(chrono::steady_clock::now().time_since_epoch().count());
ll randint(ll a, ll b) {
    return uniform_int_distribution<ll>(a, b)(mt_rng);
}
 
template<class T, class U> void vti(vt<T> &v, U x, size_t n) {
    v=vt<T>(n, x);
}
template<class T, class U> void vti(vt<T> &v, U x, size_t n, size_t m...) {
    v=vt<T>(n);
    EACH(a, v)
        vti(a, x, m);
}
 
const int d4i[4]={-1, 0, 1, 0}, d4j[4]={0, 1, 0, -1};
const int d8i[8]={-1, -1, 0, 1, 1, 1, 0, -1}, d8j[8]={0, 1, 1, 1, 0, -1, -1, -1};
 
void solve() {
    
    int n,e;
    read(n,e);
    vector<vector<int> > edges(e,vector<int> (2));
    read(edges);
    vector<vector<int> > adj(n);
    for(vector<int> v: edges){
        adj[v[0]-1].push_back(v[1]-1);
        adj[v[1]-1].push_back(v[0]-1);
    }

    vector<int> side(n,-1);
    bool isb = true;
    for(int i = 0;i<n;i++)
    if(side[i] == -1){
    queue<int> q;
    q.push(i);
    side[i] = 0;
    while(!q.empty()){
        int v = q.front();
        q.pop();

        for(int u: adj[v]){
            if(side[u] == -1){
                side[u] = side[v]^1;
                q.push(u);
            }
            else{
                isb &= side[u] != side[v];
            }
        }
    }
}
if(!isb)
    cout<<"NO";
else
    {
        cout<<"YES";
        for(vector<int> v: edges){
        if(side[v[0]-1]<side[v[1]-1])
        cout<<"0";
        else
        {
            cout<<"1";
        }
    
    }}

}
 
int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
 
    int t=1;
// /*single test case*/	read(t);
    FOR(t) {
        //write("Case #", i+1, ": ");
        solve();
        cout<<"\n";
    }
}