Problem: You are given an integer array of length n.

You have to choose some subsequence of this array of maximum length such that this subsequence forms a increasing sequence of consecutive integers. In other words the required sequence should be equal to [x, x + 1, ..., x + k - 1] for some value x and length k.

Subsequence of an array can be obtained by erasing some (possibly zero) elements from the array. You can erase any elements, not necessarily going successively. The remaining elements preserve their order. For example, for the array [5, 3, 1, 2, 4] the following arrays are subsequences: [3], [5, 3, 1, 2, 4], [5, 1, 4], but the array [1, 3] is not.

Input

The first line of the input containing integer number n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of the array. The second line of the input containing n integer numbers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the array itself.

Output

On the first line print k — the maximum length of the subsequence of the given array that forms an increasing sequence of consecutive integers.

On the second line print the sequence of the indices of the any maximum length subsequence of the given array that forms an increasing sequence of consecutive integers.

Examples

Input

7
3 3 4 7 5 6 8


Output

4
2 3 5 6 


Input

6
1 3 5 2 4 6


Output

2
1 4 


Input

4
10 9 8 7


Output

1
1 


Input

9
6 7 8 3 4 5 9 10 11


Output

6
1 2 3 7 8 9 

Note

All valid answers for the first example (as sequences of indices): 

  * [1, 3, 5, 6] 
  * [2, 3, 5, 6] 



All valid answers for the second example: 

  * [1, 4] 
  * [2, 5] 
  * [3, 6] 



All valid answers for the third example: 

  * [1] 
  * [2] 
  * [3] 
  * [4] 



All valid answers for the fourth example: 

  * [1, 2, 3, 7, 8, 9] 

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class CodeForces {
    private static void solve() {
        int n  = sc.nextInt();
        int[] arr = sc.setintArray(n);
        Map<Integer,Integer> map = new HashMap<>();     // stores the length of LIS ending at arr[i]
        int endingElement = -1;
        int maxLen = -1;
        int takenIndex = -1;
        for(int i=0;i<n;i++){
            int x = map.getOrDefault(arr[i]-1,0)+1;
            int y = map.getOrDefault(arr[i],0);
            map.put(arr[i],max2(x,y));
            if(max2(x,y)>maxLen){
                maxLen = max2(x,y);
                endingElement = arr[i];
                takenIndex = i;
            }

        }
        debug.println(map);
        out.println(maxLen);
        Deque<Integer> dq = new ArrayDeque<>();
        while (maxLen>0 && takenIndex>=0){
            if(arr[takenIndex]==endingElement){
               dq.push(takenIndex+1);
                endingElement--;
                maxLen--;
            }
            takenIndex--;

        }
        StringBuilder sb = new StringBuilder();
        while (!dq.isEmpty())sb.append(dq.pop()).append(" ");
        out.println(sb);
    }


    /*****************************************WRITING CODE ENDS HERE******************************************/

    public static void main(String[] args){
        FIO(true);
        int testCase = 1;
//        testCase = sc.nextInt();
        while (testCase-- > 0) solve();
        closeIO();
    }

    static Scanner sc ;                     // FAST INPUT
    static PrintWriter out;                // FAST OUTPUT
    static PrintWriter debug ;             // DEBUG IN FILE : debug.txt

    public static void FIO(boolean isDebug){
        sc = new Scanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
        if(isDebug)
            try {
                debug = new PrintWriter(new FileOutputStream("debug.txt"));
            }catch (IOException e){
                e.printStackTrace();
            }
    }
    public static void closeIO(){
        sc.close();
        out.flush();
        out.close();
        if(debug!=null) {
            debug.flush();
            debug.close();
        }
    }


    /**************************************HELPER FUNCTION STARTS HERE ************************************/

    public static int mod = (int) 1e9 + 7;
    public static final int INT_MAX = Integer.MAX_VALUE;
    public static final int INT_MIN = Integer.MIN_VALUE;
    public static final long LONG_MAX = Long.MAX_VALUE;
    public static final long LONG_MIN = Long.MIN_VALUE;
    public static final double DOUBLE_MAX = Double.MAX_VALUE;
    public static final double DOUBLE_MIN = Double.MIN_VALUE;
    public static final String YES = "YES";
    public static final String NO = "NO";

    public static void sort(int[] a, boolean isAscending) {
        ArrayList<Integer> temp = new ArrayList<>();
        for (int j : a) temp.add(j);
        sort(temp, isAscending);
        for (int i = 0; i < a.length; i++) a[i] = temp.get(i);
    }

    public static void sort(long[] a, boolean isAscending) {
        ArrayList<Long> temp = new ArrayList<>();
        for (long ele : a) temp.add(ele);
        sort(temp, isAscending);
        for (int i = 0; i < a.length; i++) a[i] = temp.get(i);
    }

    public static void sort(List list, boolean isAscending) {
        if (isAscending)
            Collections.sort(list);
        else Collections.sort(list, Collections.reverseOrder());
    }

    // euclidean algorithm
    public static long gcd(long a, long b) {
        // time O(max (loga ,logb))
        long x = Math.min(a, b);
        long y = Math.max(a, b);
        if (y % x == 0) return x;
        return gcd(y % x, x);
    }

    public static long lcm(long a, long b) {
        // lcm(a,b) * gcd(a,b) = a * b
        return (a / gcd(a, b)) * b;
    }

    public static long power(long x, long n) {
        // time O(logn)
        long ans = 1;
        while (n > 0) {
            if ((n & 1) == 1) {
                ans *= x;
                ans %= mod;
                n--;
            } else {
                x *= x;
                x %= mod;
                n >>= 1;
            }
        }
        return ans;
    }

    public static long factorial(long n) {
        long fact = 1L;
        for (int i = 2; i <= n; i++) fact = (fact * i) % mod;
        return fact;
    }

    public static long firstDivisor(long n) {
        if (n == 1) return n;
        for (long i = 2; i * i <= n; i++)
            if (n % i == 0) return i;
        return -1;
    }

    public static int ncr(int n, int r) {
        // time O(n+r)
        if (r > n)
            return 0;
        long[] inv = new long[r + 1];
        inv[1] = 1;
        // Getting the modular inversion
        // for all the numbers
        // from 2 to r with respect to m
        for (int i = 2; i <= r; i++) {
            inv[i] = mod - (mod / i) * inv[mod % i] % mod;
        }
        int ans = 1;
        // for 1/(r!) part
        for (int i = 2; i <= r; i++) {
            ans = (int) (((ans % mod) * (inv[i] % mod)) % mod);
        }
        // for (n)*(n-1)*(n-2)*...*(n-r+1) part
        for (int i = n; i >= (n - r + 1); i--) {
            ans = (int) (((ans % mod) * (i % mod)) % mod);
        }
        return ans;
    }

    public static long max3(long a, long b, long c) { return max2(max2(a, b), c);}

    public static long max2(long a, long b) {return Math.max(a, b);}

    public static long min3(long a, long b, long c) {return min2(min2(a, b), c);}

    public static long min2(long a, long b) { return Math.min(a, b); }

    public static int max3(int a, int b, int c) { return max2(max2(a, b), c); }

    public static int max2(int a, int b) { return Math.max(a, b); }

    public static int min3(int a, int b, int c) { return min2(min2(a, b), c); }

    public static int min2(int a, int b) {
        return Math.min(a, b);
    }

    /**************************************HELPER FUNCTION ENDS HERE ************************************/

    /*****************************************FAST INPUT STARTS HERE *************************************/


    private static class Scanner {
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        private StringTokenizer st = new StringTokenizer("");

        public String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();

        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public int[] setintArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) arr[i] = nextInt();
            return arr;
        }

        public long[] setlongArray(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) arr[i] = nextLong();
            return arr;
        }

        public int[][] set2DIntArray(int n) {
            return set2DIntArray(n, n);
        }

        public int[][] set2DIntArray(int row, int col) {
            int[][] arr = new int[row][col];
            for (int i = 0; i < row; i++)
                for (int j = 0; j < col; j++)
                    arr[i][j] = nextInt();
            return arr;
        }

        public long[][] set2DlongArray(int n) {
            return set2DlongArray(n, n);
        }

        public long[][] set2DlongArray(int row, int col) {
            long[][] arr = new long[row][col];
            for (int i = 0; i < row; i++)
                for (int j = 0; j < col; j++)
                    arr[i][j] = nextLong();
            return arr;
        }

        public char[][] set2DCharArray(int n) {
            return set2DCharArray(n, n);
        }

        public char[][] set2DCharArray(int row, int col) {
            char[][] ch = new char[row][col];
            for (int i = 0; i < row; i++)
                ch[i] = sc.next().toCharArray();
            return ch;
        }

        public void close() {
            try {
                br.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
    }
    /*****************************************FAST INPUT ENDS HERE *************************************/
}