Last One

Problem

You decide to play a weird game with your friend A, who loves gathering.

Given a set S of non-negative integers consisting of n elements that can be duplicated. Each element contained in the set S is a non-negative pi-ary number. With Steps 1 to 3 below as one turn for the set S, you and your opponent repeat the turn alternately. In each turn, operate in the order of this number.

Step 1: Remove all the elements contained in the set S once, convert each removed element to a binary number, erase 0, divide it into one or more consecutive 1s, and divide the divided part. Add all to set S.

Step 2: If Set S is empty at this time, the player currently playing this turn loses. Step 3: Select one element a contained in the set S, and subtract any integer x that satisfies 1 ≤ x ≤ a from that a.

The figure below is an example of how to proceed for the first turn given the following inputs.

Four 10 3 2 11 16 5 16 AE

The first is your turn. When both parties do their best for a given input, do you really win?

Input

The input is given in the following format:

n p1 m1 p2 m2 ... pi mi ... pn mn

N pi-ary numbers mi, which are elements of the set, are given. The number n of elements in the set does not exceed 105. Also, 2 ≤ pi ≤ 62 is satisfied. The pi-ary number mi uses 52 letters of the alphabet in addition to the usual numbers 0-9. The order is 012 ... 789 ABC ... XYZabc ... xyz in ascending order, and the characters up to the i-th are used. Also, the pi-ary mi does not exceed 218-1 in decimal.

Output

Output win if you win against the given input, lose if you lose.

Examples

Input

1 10 1

Output

win

Input

2 10 1 10 1

Output

lose

Input

3 25 53AI 43 3BI0 62 pn6

Output

win

inputFormat

inputs.

Four 10 3 2 11 16 5 16 AE

The first is your turn. When both parties do their best for a given input, do you really win?

Input

The input is given in the following format:

n p1 m1 p2 m2 ... pi mi ... pn mn

N pi-ary numbers mi, which are elements of the set, are given. The number n of elements in the set does not exceed 105. Also, 2 ≤ pi ≤ 62 is satisfied. The pi-ary number mi uses 52 letters of the alphabet in addition to the usual numbers 0-9. The order is 012 ... 789 ABC ... XYZabc ... xyz in ascending order, and the characters up to the i-th are used. Also, the pi-ary mi does not exceed 218-1 in decimal.

outputFormat

Output

Output win if you win against the given input, lose if you lose.

Examples

Input

1 10 1

Output

win

Input

2 10 1 10 1

Output

lose

Input

3 25 53AI 43 3BI0 62 pn6

Output

win

样例

1
10 1

win