Kattis

Roman Holidays

The ancient Romans created many important things: aqueducts, really straight roads, togas, those candles that spout fireworks. But the most useless is Roman numerals, a very awkward way to represent positive integers.

The Roman numeral system uses seven different letters, each representing a different numerical value: the letter I represents the value $1$, V $5$, X $10$, L $50$, C $100$, D $500$ and M $1\, 000$. These can be combined to form the following base values:

 $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ I II III IV V VI VII VIII IX X $10$ $20$ $30$ $40$ $50$ $60$ $70$ $80$ $90$ $100$ X XX XXX XL L LX LXX LXXX XC C $100$ $200$ $300$ $400$ $500$ $600$ $700$ $800$ $900$ $1\, 000$ C CC CCC CD D DC DCC DCCC CM M

The Roman numeral representation of a non-base value number $x$ is obtained by first breaking up $x$ into a sum of base values and then translating each base value, largest to smallest. When choosing base values you always choose the largest one $\leq x$ first, then the largest one $\leq$ the amount remaining, and so on. Thus $14 = 10 + 4$ = XIV, $792 = 700 + 90 + 2$ = DCCXCII. Numbers larger than $1\, 000$ use as many M’s as necessary. So $2\, 018$ = MMXVIII and $1\, 000\, 000$ would be a string of one thousand M’s (hence the word “awkward” in the first paragraph).

The Roman numeral representation gives a new way to order the positive integers. We can now order them alphabetically if we treat the Roman representation of each integer as a word. If one word $A$ is a prefix for another word $B$ then $A$ comes first. We’ll call this the roman ordering of the positive integers. Thus the first number in roman ordering is C (100 in our system). The next three numbers would be CC, CCC and CCCI, and so on.

Note in roman ordering, all numbers larger than $1\, 000$ would come before any number starting with V or X. Indeed the last number is XXXVIII. In this problem you will be given one or more positive integers and must determine their positions in the roman ordering – from the front or back as appropriate.

Input

Input starts with a positive integer $n \leq 100$ indicating the number of positive integers to follow, each on a separate line. Each of these remaining numbers will be $\leq 10^9$.

Output

For each value (other than $n$), output the position of the integer in the roman ordering, one per line. If the position is relative to the end of the roman ordering, make the integer negative. Thus $38$ has roman ordering position $-1$, $37$ has position $-2$, and so on.

Sample Input 1 Sample Output 1
3
100
101
38

1
302
-1