Problem: There are n left boots and n right boots. Each boot has a color which is denoted as a lowercase Latin letter or a question mark ('?'). Thus, you are given two strings l and r, both of length n. The character l_i stands for the color of the i-th left boot and the character r_i stands for the color of the i-th right boot.

A lowercase Latin letter denotes a specific color, but the question mark ('?') denotes an indefinite color. Two specific colors are compatible if they are exactly the same. An indefinite color is compatible with any (specific or indefinite) color.

For example, the following pairs of colors are compatible: ('f', 'f'), ('?', 'z'), ('a', '?') and ('?', '?'). The following pairs of colors are not compatible: ('f', 'g') and ('a', 'z').

Compute the maximum number of pairs of boots such that there is one left and one right boot in a pair and their colors are compatible.

Print the maximum number of such pairs and the pairs themselves. A boot can be part of at most one pair.

Input

The first line contains n (1 ≤ n ≤ 150000), denoting the number of boots for each leg (i.e. the number of left boots and the number of right boots).

The second line contains the string l of length n. It contains only lowercase Latin letters or question marks. The i-th character stands for the color of the i-th left boot.

The third line contains the string r of length n. It contains only lowercase Latin letters or question marks. The i-th character stands for the color of the i-th right boot.

Output

Print k — the maximum number of compatible left-right pairs of boots, i.e. pairs consisting of one left and one right boot which have compatible colors.

The following k lines should contain pairs a_j, b_j (1 ≤ a_j, b_j ≤ n). The j-th of these lines should contain the index a_j of the left boot in the j-th pair and index b_j of the right boot in the j-th pair. All the numbers a_j should be distinct (unique), all the numbers b_j should be distinct (unique).

If there are many optimal answers, print any of them.

Examples

Input


10
codeforces
dodivthree


Output


5
7 8
4 9
2 2
9 10
3 1


Input


7
abaca?b
zabbbcc


Output


5
6 5
2 3
4 6
7 4
1 2


Input


9
bambarbia
hellocode


Output


0


Input


10
code??????
??????test


Output


10
6 2
1 6
7 3
3 5
4 8
9 7
5 1
2 4
10 9
8 10

Solution (in JAVA):

Solution:
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;

public class round547div3D {

    boolean ONLINE_JUDGE = (System.getProperty("ONLINE_JUDGE") != null);

    public round547div3D() throws IOException {
        InputReader in;
        if (ONLINE_JUDGE) {
            in = new InputReader(System.in);
        } else {
            in = new InputReader(new FileInputStream("/Users/karj/cp/input.txt"));
        }
        PrintWriter out = new PrintWriter(System.out);

        int T = 1;
        for (int caseNo = 1; caseNo <= T; caseNo++) {
            solve(caseNo, in, out);
        }

        out.close();
    }

    private void solve(int caseNo, InputReader in, PrintWriter out) throws IOException {
        int n = in.nextInt();
        String l = in.nextString();
        String r = in.nextString();
        HashMap<Character, TreeSet<Integer>> lmap = new HashMap<>();
        HashMap<Character, TreeSet<Integer>> rmap = new HashMap<>();
        for (int i = 0; i < n; i++) {
            TreeSet<Integer> s1 = new TreeSet<>();
            if (lmap.containsKey(l.charAt(i))) {
                s1 = lmap.get(l.charAt(i));
            }
            s1.add(i + 1);
            lmap.put(l.charAt(i), s1);

            TreeSet<Integer> s2 = new TreeSet<>();
            if (rmap.containsKey(r.charAt(i))) {
                s2 = rmap.get(r.charAt(i));
            }
            s2.add(i + 1);
            rmap.put(r.charAt(i), s2);
        }
        debug(lmap);
        debug(rmap);
        StringBuilder ans = new StringBuilder("");
        int k = 0;
        for (char c = 'a'; c <= 'z'; c++) {
            TreeSet<Integer> s1 = lmap.getOrDefault(c, new TreeSet<>());
            TreeSet<Integer> s2 = rmap.getOrDefault(c, new TreeSet<>());
//            debug(c, s1, s2);
            int is = min(s1.size(), s2.size());
            for (int i = 0; i < is; i++) {
                ans.append(s1.pollFirst() + " " + s2.pollFirst() + "\n");
                k++;
            }
            if (s1.size() == 0) {
                lmap.remove(c);
            }
            if (s2.size() == 0) {
                rmap.remove(c);
            }
        }
        TreeSet<Integer> lqn = lmap.getOrDefault('?', new TreeSet<>());
        int is = lqn.size();
        for (int i = 0; i < is; i++) {
            for (Map.Entry<Character, TreeSet<Integer>> entry : rmap.entrySet()) {
                int key = entry.getKey();
                TreeSet<Integer> rqq = entry.getValue();
                if (key == '?') {
                    continue;
                }
                debug(lqn, rqq);
                int js = min(lqn.size(), rqq.size());
                for (int j = 0; j < js; j++) {
                    ans.append(lqn.pollFirst() + " " + rqq.pollFirst() + "\n");
                    k++;
                }
                if (lqn.size() == 0) {
                    lmap.remove('?');
                }
                if (rqq.size() == 0) {
                    rmap.remove(key);
                }
            }
        }
        TreeSet<Integer> rqn = rmap.getOrDefault('?', new TreeSet<>());
        is = rqn.size();
        for (int i = 0; i < is; i++) {
            for (Map.Entry<Character, TreeSet<Integer>> entry : lmap.entrySet()) {
                int key = entry.getKey();
                TreeSet<Integer> lqq = entry.getValue();
                if (key == '?') {
                    continue;
                }
                debug(rqn, lqq);
                int js = min(rqn.size(), lqq.size());
                for (int j = 0; j < js; j++) {
                    ans.append(lqq.pollFirst() + " " + rqn.pollFirst() + "\n");
                    k++;
                }
                if (rqn.size() == 0) {
                    rmap.remove('?');
                }
                if (lqq.size() == 0) {
                    lmap.remove(key);
                }
            }
        }
        for (char c = '?'; c <= '?'; c++) {
            TreeSet<Integer> s1 = lmap.getOrDefault(c, new TreeSet<>());
            TreeSet<Integer> s2 = rmap.getOrDefault(c, new TreeSet<>());
//            debug(c, s1, s2);
            is = min(s1.size(), s2.size());
            for (int i = 0; i < is; i++) {
                ans.append(s1.pollFirst() + " " + s2.pollFirst() + "\n");
                k++;
            }
            if (s1.size() == 0) {
                lmap.remove(c);
            }
            if (s2.size() == 0) {
                rmap.remove(c);
            }
        }
        out.println(k);
        if (k > 0) {
            out.print(ans);
        }
    }

    static class InputReader {

        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public interface SpaceCharFilter {

            public boolean isSpaceChar(int ch);
        }

        public String next() {
            return nextString();
        }

        public String nextString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public Long nextLong() {
            return Long.parseLong(nextString());
        }

        public Double nextDouble() {
            return Double.parseDouble(nextString());
        }

        public char nextCharacter() {
            return nextString().charAt(0);
        }

        public int[] nextIntArray(int N) {
            int A[] = new int[N];
            for (int i = 0; i < N; i++) {
                A[i] = nextInt();
            }
            return A;
        }

        public long[] nextLongArray(int N) {
            long A[] = new long[N];
            for (int i = 0; i < N; i++) {
                A[i] = nextLong();
            }
            return A;
        }

        public double[] nextDoubleArray(int N) {
            double A[] = new double[N];
            for (int i = 0; i < N; i++) {
                A[i] = nextDouble();
            }
            return A;
        }
    }

    int min(int... a) {
        int min = Integer.MAX_VALUE;
        for (int v : a) {
            min = Math.min(min, v);
        }
        return min;
    }

    long min(long... a) {
        long min = Long.MAX_VALUE;
        for (long v : a) {
            min = Math.min(min, v);
        }
        return min;
    }

    double min(double... a) {
        double min = Double.MAX_VALUE;
        for (double v : a) {
            min = Math.min(min, v);
        }
        return min;
    }

    int max(int... a) {
        int max = Integer.MIN_VALUE;
        for (int v : a) {
            max = Math.max(max, v);
        }
        return max;
    }

    long max(long... a) {
        long max = Long.MIN_VALUE;
        for (long v : a) {
            max = Math.max(max, v);
        }
        return max;
    }

    double max(double... a) {
        double max = Double.MIN_VALUE;
        for (double v : a) {
            max = Math.max(max, v);
        }
        return max;
    }

    public <A, B> Pair MP(A a, B b) {
        return new Pair<A, B>(a, b);
    }

    class Pair<F, S> {
        public final F f;
        public final S s;

        public Pair(F f, S s) {
            this.f = f;
            this.s = s;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Pair<?, ?> pair = (Pair<?, ?>) o;
            return Objects.equals(f, pair.f) &&
                    Objects.equals(s, pair.s);
        }

        @Override
        public int hashCode() {

            return Objects.hash(f, s);
        }

        @Override
        public String toString() {
            return f.toString() + " " + s.toString();
        }
    }


    private void debug(Object... o) {
        if (ONLINE_JUDGE) {
            return;
        }
        System.err.println(Arrays.deepToString(o));
    }

    public static void main(String args[]) throws IOException {
        new round547div3D();
    }
}