using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

public class BlindAbacus : IEnumerable<BlindAbacus.Row>
{
    public int n;
    public int rows;
    public Row[] data;
    private List<WeakReference> enumerators = new List<WeakReference>();

    public BlindAbacus(int n, int rows)
    {
        this.n = n;
        this.rows = rows;
        this.data = new Row[rows];
        for (int i = 0; i < rows; i++)
        {
            data[i] = new Row(n-1);
        }
    }

    public BlindAbacus(int n, int value, bool x)
    {
        // count rows
        int rows;
        int[] initialData;
        if (value != 0)
        {
            rows = 1;
            int valueAtNextRow = n;
            while (valueAtNextRow <= value)
            {
                rows++;
                valueAtNextRow *= n;
            }

            // prepare data
            initialData = new int[rows];

            for (int i = rows - 1; i >= 0; i--)
            {
                int tmp = 0;
                initialData[i] = 0;
                while (tmp + (int)Math.Pow(n, i) <= value && initialData[i] <= n - 1)
                {
                    tmp += (int)Math.Pow(n, i);
                    initialData[i]++;
                }
                value -= (int)Math.Pow(n, i) * initialData[i];
            }
        }
        else
        {
            rows = 0;
            initialData = new int[1];
        }
        this.n = n;
        this.rows = rows;
        this.data = new Row[rows];
        for (int i = 0; i < rows; i++)
        {
            data[i] = new Row(n - 1);
            data[i].add(initialData[i]);
        }
    }

    public override string ToString()
    {
        string result = "";

        for (int i = rows - 1; i >= 0; i--)
        {
            result += data[i].ToString();
            if (i != 0) result += "\n";
        }

        return result;
    }

    public Row this[int i]
    {
        get
        {
            return data[i];
        }

        set
        {
            this.data[i] = value;
        }
    }

    public static explicit operator int(BlindAbacus abacus)
    {
        int result = 0;
        int x = 1;

        for (int i = 0; i < abacus.rows; i++, x = x * abacus.n)
        {
            result += abacus[i].State*x;
        }

        return result;
    }

    public static BlindAbacus operator +(BlindAbacus a, BlindAbacus b)
    {
        if (a.n == b.n)
        {
            return new BlindAbacus(a.n, (int)a+(int)b, true);
        }
        else throw new ComputationException();
    }

    public static BlindAbacus operator -(BlindAbacus a, BlindAbacus b)
    {
        if (a.n == b.n)
        {
            return new BlindAbacus(a.n, (int)a-(int)b, true);
        }
        else throw new ComputationException();
    }

    public static BlindAbacus operator ++(BlindAbacus a)
    {
        return new BlindAbacus(a.n, (int)a+1, true);
    }

    public static BlindAbacus operator --(BlindAbacus a)
    {
        if ((int)a > 0)
        {
            return new BlindAbacus(a.n, (int)a - 1, true);
        }
        else throw new ComputationException();
    }

    // enumerator
    public IEnumerator<BlindAbacus.Row> GetEnumerator()
    {
        BlindAbacusEnumerator enumerator = new BlindAbacusEnumerator(this);
        enumerators.Add(new WeakReference(enumerator));
        return enumerator;
    }
    System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator()
    {
        return GetEnumerator();
    }


    // internal classes
    public class Row
    {
        int rowSize;
        int state;

        public Row(int rowSize)
        {
            this.rowSize = rowSize;
            this.state = 0;
        }

        public void add(int x)
        {
            if (state < rowSize) {
                state += x;
            } else throw new IncorrectRowValueException();
        }
        public void remove(int x)
        {
            if (state != 0)
            {
                state -= x;
            }
            else throw new IncorrectRowValueException();
        }

        public int State {
            get {
                return state;
            }
        }

        public override string ToString()
        {
            string result = "";

            for (int i = 0; i < 2*rowSize; i++) {
                if (i < state || i >= state+rowSize) {
                    result += "I";
                } else {
                    result += "-";
                }
            }

            return result;
        }
    }

    public class BlindAbacusEnumerator : IEnumerator<BlindAbacus.Row>
    {
        private readonly BlindAbacus outer;
        public int i = -1;

        internal BlindAbacusEnumerator(BlindAbacus outer) {
            this.outer = outer;
        }

        public BlindAbacus.Row Current
        {
            get { return outer.data[i]; }
        }

        void System.Collections.IEnumerator.Reset()
        {
            this.i = -1;
        }

        bool System.Collections.IEnumerator.MoveNext()
        {
            foreach (WeakReference reference in outer.enumerators) {
                if (reference != null && (reference.Target as BlindAbacusEnumerator).i == i+1)
                {
                    throw new SomeoneThereException();
                }
            }
            if (++i < outer.data.Length) return true;
            return false;
        }

        void IDisposable.Dispose() {
            WeakReference toRemove = null;
            foreach (WeakReference reference in outer.enumerators)
            {
                if (reference != null && (reference.Target as BlindAbacusEnumerator) == this)
                {
                    toRemove = reference;
                }
            }
            outer.enumerators.Remove(toRemove);
        }

        object System.Collections.IEnumerator.Current
        {
            get { return outer.data[i]; }
        }
    }

    public class IncorrectRowValueException : Exception { }
    public class ComputationException : Exception { }
    public class SomeoneThereException : Exception { }
}