def almostIncreasingSequence(sequence):
    i = 0  # An iterator for our given list
    while i <= len(sequence):
        mod_sequence = []
        if i>1:
            mod_sequence = sequence[0:(i-1)]+sequence[i:]  # Concatenate two lists, each excluding the active element
        elif i == len(sequence)-1:
            mod_sequence = sequence[:-1]
        else:
            mod_sequence = sequence[i:]
        if checkSequence(mod_sequence):  # Check to see if it is a sequence
            return True
        i+= 1
    return False


def checkSequence(sequence):
    i = 0
    while i < len(sequence)-1:
        if sequence[i] >= sequence[i+1]:
            return False
        i += 1
    return True