Food Composition

Food packaging lists the ingredients a product is made of, and they are always given in order of decreasing content: the ingredient present in the largest amount is written first, then the second-largest, and so on. For some ingredients the exact amount is stated, but for others it is not.

Each content value is measured in percent, is a multiple of $0.1%$, and every ingredient makes up at least $0.1%$ of the product. The listed ingredients make up the entire product, so their percentages add up to exactly $100%$. Because the list is in strictly decreasing order, every ingredient has a strictly smaller percentage than the one before it (no two are equal).

Given the ingredient list, determine for each ingredient the minimum and the maximum percentage it could possibly have.

The first line contains the number of ingredients $N$ ($1 \le N \le 45$).

Each of the next $N$ lines describes one ingredient, in order of decreasing content. A line is either just the ingredient's name, or the name followed by a single space and its stated content. Names consist of the letters A–Z and a–z and are at most $20$ characters long. A stated content is a percentage that is a multiple of $0.1$.

Print the ingredients in the given order, one per line: the name followed by its minimum and its maximum possible content, separated by single spaces. Print every number with exactly one digit after the decimal point, using a period as the decimal separator.

If the given list is impossible (no valid assignment of percentages exists), print a single line containing EI SAA instead.