Problem: There are quite a lot of ways to have fun with inflatable balloons. For example, you can fill them with water and see what happens.

Grigory and Andrew have the same opinion. So, once upon a time, they went to the shop and bought n packets with inflatable balloons, where i-th of them has exactly a_i balloons inside.

They want to divide the balloons among themselves. In addition, there are several conditions to hold:

  * Do not rip the packets (both Grigory and Andrew should get unbroken packets); 
  * Distribute all packets (every packet should be given to someone); 
  * Give both Grigory and Andrew at least one packet; 
  * To provide more fun, the total number of balloons in Grigory's packets should not be equal to the total number of balloons in Andrew's packets. 



Help them to divide the balloons or determine that it's impossible under these conditions.

Input

The first line of input contains a single integer n (1 ≤ n ≤ 10) — the number of packets with balloons.

The second line contains n integers: a_1, a_2, …, a_n (1 ≤ a_i ≤ 1000) — the number of balloons inside the corresponding packet.

Output

If it's impossible to divide the balloons satisfying the conditions above, print -1.

Otherwise, print an integer k — the number of packets to give to Grigory followed by k distinct integers from 1 to n — the indices of those. The order of packets doesn't matter.

If there are multiple ways to divide balloons, output any of them.

Examples

Input

3
1 2 1


Output

2
1 2


Input

2
5 5


Output

-1


Input

1
10


Output

-1

Note

In the first test Grigory gets 3 balloons in total while Andrey gets 1.

In the second test there's only one way to divide the packets which leads to equal numbers of balloons.

In the third test one of the boys won't get a packet at all.

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;

public class Tester {

    public static void main(String[] args) {
        final int mod = (int) (1e9 + 7);
        final InputReader in = new InputReader(System.in);
        final PrintWriter out = new PrintWriter(System.out);

        final int n = in.nextInt();
        final int[] arr = new int[n];
        int min = Integer.MAX_VALUE;
        int minI = 0;
        for (int i = 0; i < n; i++) {
            arr[i] = in.nextInt();
            if (min > arr[i]) {
                min = arr[i];
                minI = i;
            }
        }

        if (n > 2) {
            out.println(1);
            out.println(minI + 1);
        } else {
            if (n == 1) {
                out.println(-1);
            } else {
                if (arr[0] == arr[1]) {
                    out.println(-1);
                } else {
                    out.println(1);
                    out.println(1);
                }
            }
        }

        out.close();

    }

    static long fac(long a) {
        long k = a;
        for (long i = 2; i < a; i++) {
            k = k * i;
        }
        System.out.println(k + " " + a);

        return a;

    }

    static class Pair implements Comparable<Pair> {

        int x, y;
        // int i;

        Pair(int x, int y) {
            this.x = x;
            this.y = y;
            // this.i = i;
        }

        @Override
        public int compareTo(Pair o) {
            if (this.x != o.x) {
                return Long.compare(this.x, o.x);
            } else {
                return Long.compare(this.y, o.y);
                // return 0;
            }
        }

        @Override
        public boolean equals(Object o) {
            if (o instanceof Pair) {
                final Pair p = (Pair) o;
                return p.x == x && p.y == y;// && p.i == i;
            }
            return false;
        }
    }

    public static boolean isPal(String s) {
        for (int i = 0, j = s.length() - 1; i <= j; i++, j--) {
            if (s.charAt(i) != s.charAt(j)) {
                return false;
            }
        }
        return true;
    }

    public static String rev(String s) {
        final StringBuilder sb = new StringBuilder(s);
        sb.reverse();
        return sb.toString();
    }

    public static long gcd(long x, long y) {
        if (x % y == 0) {
            return y;
        } else {
            return gcd(y, x % y);
        }
    }

    public static int gcd(int x, int y) {
        if (x % y == 0) {
            return y;
        } else {
            return gcd(y, x % y);
        }
    }

    public static long gcdExtended(long a, long b, long[] x) {

        if (a == 0) {
            x[0] = 0;
            x[1] = 1;
            return b;
        }
        final long[] y = new long[2];
        final long gcd = gcdExtended(b % a, a, y);

        x[0] = y[1] - (b / a) * y[0];
        x[1] = y[0];

        return gcd;
    }

    public static int abs(int a, int b) {
        return Math.abs(a - b);
    }

    public static long abs(long a, long b) {
        return Math.abs(a - b);
    }

    public static int max(int a, int b) {
        if (a > b) {
            return a;
        } else {
            return b;
        }
    }

    public static int min(int a, int b) {
        if (a > b) {
            return b;
        } else {
            return a;
        }
    }

    public static long max(long a, long b) {
        if (a > b) {
            return a;
        } else {
            return b;
        }
    }

    public static long min(long a, long b) {
        if (a > b) {
            return b;
        } else {
            return a;
        }
    }

    public static long pow(long n, long p, long m) {
        long result = 1;
        if (p == 0) {
            return 1;
        }
        if (p == 1) {
            return n;
        }
        while (p != 0) {
            if (p % 2 == 1) {
                result *= n;
            }
            if (result >= m) {
                result %= m;
            }
            p >>= 1;
            n *= n;
            if (n >= m) {
                n %= m;
            }
        }
        return result;
    }

    public static long pow(long n, long p) {
        long result = 1;
        if (p == 0) {
            return 1;
        }
        if (p == 1) {
            return n;
        }
        while (p != 0) {
            if (p % 2 == 1) {
                result *= n;
            }
            p >>= 1;
            n *= n;
        }
        return result;
    }

    static class InputReader {

        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;

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

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

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

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

        public int[] nextIntArray(int n) {
            final int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

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

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

        public String nextLine() {
            int c = snext();
            while (isSpaceChar(c)) {
                c = snext();
            }
            final StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
}