# sign function
def sgn(x):
    if x>=0:
        return 1
    return -1

# check whether a number is an integer (with tolerance)
def isint_nonzero(x):
    if abs(x)<1e-11:
        return False
    return abs(round(x)-x)<1e-11

# find the common substring in a list of strings
def common_substr(strings):
    out=""
    if len(strings)==0:
        return out
    for i in range(len(strings[0])):
        for j in range(1,len(strings)):
            if strings[j][i]!=strings[0][i]:
                return out
        out+=strings[0][i]

    return out