Create a program that inputs the vertex information of two polygons inscribed in one circle and outputs the magnitude relationship of their areas.

Assume that each vertex of the X-side is numbered counterclockwise from 1 to X (the figure shows an example when X = 4). However, the given polygon assumes that the center of the circle is contained inside, and the data on the position of vertex i is the angle v (1 ≤ v <180) of the central angle measured counterclockwise from vertex i to vertex i + 1. Integer). Regarding the magnitude relationship to be output, 1 (half-width number) when the area of ​​the first polygon is large, 2 (half-width number) when the area of ​​the second polygon is large, and when the areas are the same, Please output 0 (half-width number).

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Input

A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. Each dataset is given in the following format:


m
v1
v2
::
vm −1
n
v1
v2
::
vn − 1


The first line gives the number of vertices of the first polygon m (3 ≤ m ≤ 50), and the following m − 1 line gives the information vi (1 ≤ vi <180) of the vertices i of the first polygon. ..

The following line gives the number of vertices n (3 ≤ n ≤ 50) of the second polygon, and the following n − 1 line gives the information vi (1 ≤ vi <180) for the vertices i of the second polygon.

The number of datasets does not exceed 200.

Output

Outputs the magnitude relationship (half-width numbers) for each data set on one line.

Example

Input

4
30
125
75
4
30
125
75
5
30
125
75
65
4
30
125
75
4
30
125
75
6
30
50
50
25
75
0


Output

0
1
2
# Area of Polygon

from math import sin
from math import radians

while True:
    m = int(raw_input())
    if m == 0:
        break

    a1, v, vv = (0.0, 0, 0)
    for i in range(m):
        if i < m - 1:
            v = int(raw_input())
            vv += v
        else:
            v = 360 - vv
        a1 += sin(radians(v)) * 100 / 2

    n = int(raw_input())

    a2, v, vv = (0.0, 0, 0)
    for i in range(n):
        if i < n - 1:
            v = int(raw_input())
            vv += v
        else:
            v = 360 - vv
        a2 += sin(radians(v)) * 100 / 2

    if a1 > a2:
        print 1
    elif a1 < a2:
        print 2
    else:
        print 0