This is a hard version of the problem. The actual problems are different, but the easy version is almost a subtask of the hard version. Note that the constraints and the output format are different.

You are given a string s consisting of n lowercase Latin letters.

You have to color all its characters the minimum number of colors (each character to exactly one color, the same letters can be colored the same or different colors, i.e. you can choose exactly one color for each index in s).

After coloring, you can swap any two neighboring characters of the string that are colored different colors. You can perform such an operation arbitrary (possibly, zero) number of times.

The goal is to make the string sorted, i.e. all characters should be in alphabetical order.

Your task is to find the minimum number of colors which you have to color the given string in so that after coloring it can become sorted by some sequence of swaps. Note that you have to restore only coloring, not the sequence of swaps.

Input

The first line of the input contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of s.

The second line of the input contains the string s consisting of exactly n lowercase Latin letters.

Output

In the first line print one integer res (1 ≤ res ≤ n) — the minimum number of colors in which you have to color the given string so that after coloring it can become sorted by some sequence of swaps.

In the second line print any possible coloring that can be used to sort the string using some sequence of swaps described in the problem statement. The coloring is the array c of length n, where 1 ≤ c_i ≤ res and c_i means the color of the i-th character.

Examples

Input


9
abacbecfd


Output


2
1 1 2 1 2 1 2 1 2 


Input


8
aaabbcbb


Output


2
1 2 1 2 1 2 1 1


Input


7
abcdedc


Output


3
1 1 1 1 1 2 3 


Input


5
abcde


Output


1
1 1 1 1 1 
import java.io.DataInputStream; 
import java.io.FileInputStream; 
import java.io.IOException; 
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Scanner; 
import java.util.StringTokenizer; 
import java.io.BufferedReader; 
import java.util.*;
import java.math.BigInteger; 


public class StringColoringhard{
	public static FastReader fs = new FastReader();
	
	static PrintWriter out = new PrintWriter(System.out);
	
	static void solve() {
		StringBuffer output = new StringBuffer();
		int n = fs.nextInt();
		char string [] = fs.next().toCharArray();
		int max_till_now [] = new int [26];
		Arrays.fill(max_till_now, 0);
		ArrayList<Integer> ans = new ArrayList<>();
		ans.add(0);
		int c = 'a' - 1,d = string[0];
		int colors_used = 1;
		for(int i = 1; i<n; i++) {
			if(string[i] >= d) {
				ans.add(0);
				d = string[i];
			}
			else {
				int color = 0;
				for(int j = string[i]+1; j<d+1; j++) {
					color = max(color,max_till_now[j-'a']);
				}
				ans.add(color+1);
				max_till_now[string[i]-'a'] = max(max_till_now[string[i]-'a'],color+1);
				colors_used = max(colors_used,color+2);
			}
		}
		out.println(colors_used);
		for(int x : ans)
			out.print(x+1 + " ");
		out.println();
	}
	
	public static void main(String[] args) {
		Thread t = new Thread(null,null,"",1 << 28) {
			public void run() {
				int test_case = 1;
				//test_case = fs.nextInt();
				for(int cs = 1; cs <= test_case; cs++) {
					solve();
				}
				out.close();
			}
		};
		t.start();
		try {
			t.join();
		} catch (InterruptedException e) {
			e.printStackTrace();
		}
	}
	static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
	
	static int ceil(int x,int y) {
		return (x % y == 0 ? x / y : (x / y +1));
	}
	
	static long ceil(long x,long y) {
		return (x % y == 0 ? x / y : (x / y +1));
	}
	
	static int max(int x,int y) {
		return Math.max(x, y);
	}
	
	static int min(int x,int y) {
		return Math.min(x, y);
	}
	
	static long max(long x,long y) {
		return Math.max(x, y);
	}
	
	static long min(long x,long y) {
		return Math.min(x, y);
	}
	
	static int min(int a []) {
		int x = 1_000_000_00_9;
		for(int i = 0; i<a.length; i++)x = min(x,a[i]);
		return x;
	}
	
	static int max(int a []) {
		int x = -1_000_000_00_9;
		for(int i = 0; i<a.length; i++)x = max(x,a[i]);
		return x;
	}
	
	static long min(long a []) {
		long x = (long)3e18;
		for(int i = 0; i<a.length; i++)x = min(x,a[i]);
		return x;
	}
	
	static long max(long a []) {
		long x = -(long)3e18;
		for(int i = 0; i<a.length; i++)x = max(x,a[i]);
		return x;
	}
	
	static int power(int x,int y) {
		int res = 1;
		while(y > 0) {
			if( y % 2 == 1)res = (res * x);
			y >>= 1;
            x = (x * x);
		}
		return res;
	}
	
	static long power(long x,long y) {
		long res = 1;
		while(y > 0) {
			if( y % 2 == 1)res = (res * x);
			y >>= 1;
            x = (x * x);
		}
		return res;
	}
	
	static long power(long x,long y,long mod) {
		long res = 1;
		x %= mod;
		while(y > 0) {
			if( y % 2 == 1)res = (res * x) % mod;
			y >>= 1;
            x = (x * x) % mod;
		}
		return res;
	}
	
	static void intsort(int [] a) {
		List<Integer> temp = new ArrayList<Integer>();
		for(int i = 0; i<a.length; i++)temp.add(a[i]);
		Collections.sort(temp);
		for(int i = 0; i<a.length; i++)a[i] = temp.get(i);
	}
	
	static void longsort(long [] a) {
		List<Long> temp = new ArrayList<Long>();
		for(int i = 0; i<a.length; i++)temp.add(a[i]);
		Collections.sort(temp);
		for(int i = 0; i<a.length; i++)a[i] = temp.get(i);
	}
	
	static void reverseintsort(int [] a) {
		List<Integer> temp = new ArrayList<Integer>();
		for(int i = 0; i<a.length; i++)temp.add(a[i]);
		Collections.sort(temp);
		Collections.reverseOrder();
		for(int i = 0; i<a.length; i++)a[i] = temp.get(i);
	}
	
	static void reverselongsort(long [] a) {
		List<Long> temp = new ArrayList<Long>();
		for(int i = 0; i<a.length; i++)temp.add(a[i]);
		Collections.sort(temp);
		Collections.reverseOrder();
		for(int i = 0; i<a.length; i++)a[i] = temp.get(i);
	}
	
	static void intpairsort(intpair [] a) {
		List<intpair> temp = new ArrayList<intpair>();
		for(int i = 0; i<a.length; i++)temp.add(a[i]);
		Collections.sort(temp,(p1,p2) -> {
			if(p1.x == p2.x) return p1.y >= p2.y ? -1 : 1;
			else return p1.x > p2.x ? -1 : 1;
		});
		for(int i = 0; i<a.length; i++)a[i] = temp.get(i);
	}
	
	static void longpairsort(longpair [] a) {
		List<longpair> temp = new ArrayList<longpair>();
		for(int i = 0; i<a.length; i++)temp.add(a[i]);
		Collections.sort(temp,(p1,p2) -> {
			if(p1.x == p2.x) return p1.y >= p2.y ? -1 : 1;
			else return p1.x > p2.x ? -1 : 1;
		});
		for(int i = 0; i<a.length; i++)a[i] = temp.get(i);
	}
	
	static class intpair{
		public int x;
		public int y;
		
		intpair(int a,int b){
			this.x = a;
			this.y = b;
		}
		
		intpair(){}
	}
	
	static class longpair{
		public long x;
		public long y;
		
		longpair(long a,long b){
			this.x = a;
			this.y = b;
		}
		
		longpair(){}
	}
	
	static class data{
		public long sum;
		
		data(long val){
		    this.sum = val;
		}
		
		data(){}
		
		data combine(data l, data r) {
		    data res = new data();
		    res.sum = l.sum + r.sum;
		    return res;
		}
	}
	
	static class Seg_Tree extends data{
		public int n;
		data [] seg;
		
		Seg_Tree(int sz){
			this.n = sz;
			seg = new data[4*n+4];
		}
		
		void build(long a[], int v, int tl, int tr) {
		    if (tl == tr) {
		        seg[v] = new data(a[tl]);
		    } else {
		        int tm = (tl + tr) / 2;
		        build(a, v*2, tl, tm);
		        build(a, v*2+1, tm+1, tr);
		        seg[v] = combine(seg[v*2],seg[v*2+1]);
		    }
		}

		void update(int v, int tl, int tr, int pos, long new_val) {
		    if (tl == tr) {
		        seg[v] = new data(new_val);
		    } else {
		        int tm = (tl + tr) / 2;
		        if (pos <= tm)
		            update(v*2, tl, tm, pos, new_val);
		        else
		            update(v*2+1, tm+1, tr, pos, new_val);
		        seg[v] = combine(seg[v*2],seg[v*2+1]);
		    }
		}
		
		data query(int v, int tl, int tr, int l, int r) {
		    if (l > r) 
		        return new data(0);
		    if (l == tl && r == tr) 
		        return seg[v];
		    int tm = (tl + tr) / 2;
		    return combine(query(v*2, tl, tm, l, min(r, tm)),query(v*2+1, tm+1, tr, max(l, tm+1), r));
		}
	}
	
	static class Bit_Tree{
		static int n;
		static int [] bit;
		
		Bit_Tree(int sz){
			Bit_Tree.n = sz;
			Bit_Tree.bit = new int[n+1];
		}
		
		static int child(int x) {
			return x + (x & (-x));
		}
		
		static int parent(int x) {
			return x - (x & (-x));
		}
		
		static void build(int [] a) {
			for(int i = 0; i<a.length; i++) {
				int start = i+1;
				while(start <= n) {
					bit[start] += a[i];
					start = child(start);
				}
			}
		}
		
		static void update(int idx,int new_val) {
			idx += 1;
			while(idx <= n) {
				bit[idx] += new_val;
				idx = child(idx);
			}
		}
		
		static int query(int right) {
			int res = 0;
			while(right > 0) {
				res += bit[right];
				right = parent(right);
			}
			return res;
		}
		
		static int query(int left,int right) {
			return query(right) - query(left-1);
		}
	}
	
	public static int gcd(int a, int b)  
    { 
        BigInteger b1 = BigInteger.valueOf(a); 
        BigInteger b2 = BigInteger.valueOf(b); 
        BigInteger gcd = b1.gcd(b2); 
            return gcd.intValue(); 
    } 
      
    public static long gcd(long a, long b)  
    { 
        BigInteger b1 = BigInteger.valueOf(a); 
        BigInteger b2 = BigInteger.valueOf(b); 
        BigInteger gcd = b1.gcd(b2); 
            return gcd.longValue(); 
    } 
}