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.util.*;
import java.io.*;

public class Main {
	public static long gcd(long n, long m){ if(m > n) return gcd(m,n); if(m == 0) return n; return gcd(m, n%m);}
	public static long lcm(long m, long n){ return (m/gcd(m,n))*n;}
	static int mod = 1000000007;
	static int INF = Integer.MAX_VALUE;
	static int[] dx = {0,0,1,-1};
	static int[] dy = {1,-1,0,0};
	static int[] dx8 = {0,0,1,-1,1,1,-1,-1};
	static int[] dy8 = {1,-1,0,0,1,-1,-1,1};
	public static void main(String[] args){
		FastScanner scanner = new FastScanner();
		int n = scanner.nextInt();
		String s = scanner.next();
		int[] a = new int[n];
		for(int i = 0; i < n; i++){
			a[i] = s.charAt(i)-'a';
			//System.out.print(a[i]+" ");
		}
		int[] c = new int[n];
		TreeSet<Integer>[] set = new TreeSet[26];
		for(int i = 0; i < 26; i++){
			set[i] = new TreeSet<Integer>();
		}
		for(int i = 0; i < n; i++){
			int max = 0;
			for(int j = a[i]+1; j < 26; j++){
				if(set[j].size() == 0) continue;
				max = Math.max(max,set[j].last());
			}
			if(max == 0){
				set[a[i]].add(1);
				c[i] = 1;
			}else{
				set[a[i]].add(max+1);
				c[i] = max+1;
			}
		}
		int color = 0;
		for(int i = 0; i < n; i++){
			color = Math.max(c[i],color);
		}
		System.out.println(color);
		for(int i = 0; i < n; i++){
			System.out.print(c[i]+" ");
		}
	}

	static class Pair2 implements Comparable<Pair2>{
		long first;
		long second;
		Pair2(long first, long second){
			this.first = first;
			this.second = second;
		}
		@Override
		public int compareTo(Pair2 p){
			return Long.valueOf(first).compareTo(Long.valueOf(p.first));
		}
	}
	static class Edge2 implements Comparable<Edge2>{
		int from;
		int to;
		double cost;
		Edge2(int from, int to, double cost){
			this.from = from;
			this.to = to;
			this.cost = cost;
		}
		public int compareTo(Edge2 e){
			return Double.compare(cost,e.cost);
		}
	}
	// tar の方が数字が大きいかどうか
	static boolean compare(String tar, String src) {
		if (src == null) return true;
		if (src.length() == tar.length()) {
			int len = tar.length();
			for (int i = 0; i < len; i++) {
				if (src.charAt(i) > tar.charAt(i)) {
					return false;
				} else if (src.charAt(i) < tar.charAt(i)) {
					return true;
				}
			}
			return tar.compareTo(src) > 0 ? true : false;
		} else if (src.length() < tar.length()) {
			return true;
		} else if (src.length() > tar.length()) {
			return false;
		}
		return false;
	}
	static class RMQ {
		private int size_, dat[];
		private int query_(int a, int b, int k, int l, int r) {
			if(r <= a || b <= l) return 2147483647;
			if(a <= l && r <= b) return dat[k];
			int lc = query_(a, b, 2 * k, l, (l + r) / 2);
			int rc = query_(a, b, 2 * k + 1, (l + r) / 2, r);
			return Math.min(lc, rc);
		}
		RMQ(int s) {
			for(size_ = 1; size_ < s;) size_ *= 2;
			dat = new int[size_ * 2];
			for(int i = 0; i < size_ * 2; i++) dat[i] = 2147483647;
		}
		public void update(int pos, int x) {
			pos += size_; dat[pos] = x;
			while(pos > 1) {
				pos /= 2;
				dat[pos] = Math.min(dat[2 * pos], dat[2 * pos + 1]);
			}
		}
		public int query(int l, int r) {
			return query_(l, r, 1, 0, size_);
		}
	}
	static int size = 2100000;
	static long[] fac = new long[size];
	static long[] finv = new long[size];
	static long[] inv = new long[size];
	//繰り返し二乗法
	public static long pow(long x, long n){
		long ans = 1;
		while(n > 0){
			if((n & 1) == 1){
				ans = ans * x;
				ans %= mod;
			}
			x = x * x % mod;
			n >>= 1;
		}
		return ans;
	}
	public static long div(long x, long y){
		return (x*pow(y, mod-2))%mod;
	}
	//fac, inv, finvテーブルの初期化、これ使う場合はinitComb()で初期化必要
	public static  void initComb(){
		fac[0] = finv[0] = inv[0] = fac[1] = finv[1] = inv[1] = 1;
		for (int i = 2; i < size; ++i) {
			fac[i] = fac[i - 1] * i % mod;
			inv[i] = mod - (mod / i) * inv[(int) (mod % i)] % mod;
			finv[i] = finv[i - 1] * inv[i] % mod;
		}
	}
	//nCk % mod
	public static long comb(int n, int k){
		return fac[n] * finv[k] % mod * finv[n - k] % mod;
	}
	//n! % mod
	public static long fact(int n){
		return fac[n];
	}
	//(n!)^-1 with % mod
	public static long finv(int n){
		return finv[n];
	}

	static class Pair implements Comparable<Pair>{
    int first, second;
    Pair(int a, int b){
        first = a;
        second = b;
    }
    @Override
    public boolean equals(Object o){
        if (this == o) return true;
        if (!(o instanceof Pair)) return false;
        Pair p = (Pair) o;
        return first == p.first && second == p.second;
    }
    @Override
    public int compareTo(Pair p){
        //return first == p.first ? second - p.second : first - p.first; //firstで昇順にソート
        //return (first == p.first ? second - p.second : first - p.first) * -1; //firstで降順にソート
        return second == p.second ? first - p.first : second - p.second;//secondで昇順にソート
        //return (second == p.second ? first - p.first : second - p.second)*-1;//secondで降順にソート
		    //return first * 1.0 / second > p.first * 1.0 / p.second ? 1 : -1; // first/secondの昇順にソート
		    //return first * 1.0 / second < p.first * 1.0 / p.second ? 1 : -1; // first/secondの降順にソート
				//return second * 1.0 / first > p.second * 1.0 / p.first ? 1 : -1; // second/firstの昇順にソート
		    //return second * 1.0 / first < p.second * 1.0 / p.first ? 1 : -1; // second/firstの降順にソート
				//return Math.atan2(second, first) > Math.atan2(p.second, p.first) ? 1 : -1; // second/firstの昇順にソート
				//return first + second > p.first + p.second ? 1 : -1; //first+secondの昇順にソート
				//return first + second < p.first + p.second ? 1 : -1; //first+secondの降順にソート
				//return first - second < p.first - p.second ? 1 : -1; //first-secondの降順にソート
				//return second - first < p.second - p.first ? 1 : -1; //first-secondの昇順にソート
				//return second - first < p.second - p.first ? -1 : 1; //second-firstの昇順にソート
				//return Math.atan2(second,first) > Math.atan2(p.second, p.first) ? 1 : -1;
		}
  }

	private static class FastScanner {
		private final InputStream in = System.in;
		private final byte[] buffer = new byte[1024];
		private int ptr = 0;
		private int buflen = 0;
		private boolean hasNextByte() {
				if (ptr < buflen) {
						return true;
				}else{
						ptr = 0;
						try {
								buflen = in.read(buffer);
						} catch (IOException e) {
								e.printStackTrace();
						}
						if (buflen <= 0) {
								return false;
						}
				}
				return true;
		}
		private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
		private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
		public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
		public String next() {
				if (!hasNext()) throw new NoSuchElementException();
				StringBuilder sb = new StringBuilder();
				int b = readByte();
				while(isPrintableChar(b)) {
						sb.appendCodePoint(b);
						b = readByte();
				}
				return sb.toString();
		}
		public long nextLong() {
				if (!hasNext()) throw new NoSuchElementException();
				long n = 0;
				boolean minus = false;
				int b = readByte();
				if (b == '-') {
						minus = true;
						b = readByte();
				}
				if (b < '0' || '9' < b) {
						throw new NumberFormatException();
				}
				while(true){
						if ('0' <= b && b <= '9') {
								n *= 10;
								n += b - '0';
						}else if(b == -1 || !isPrintableChar(b)){
								return minus ? -n : n;
						}else{
								throw new NumberFormatException();
						}
						b = readByte();
				}
		}
		public int nextInt() {
				long nl = nextLong();
				if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
				return (int) nl;
		}
		public double nextDouble() { return Double.parseDouble(next());}
	}
}
