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def cache_init(num_steps , cache_interval = 3 , max_order = 1 , first_enhance = 2 , end_enhance = 24):
'''
Initialization for cache.
'''
cache_dic = {}
cache = {}
cache[-1]={}
cache_dic['cache_counter'] = 0
cache[-1]['final'] = {}
cache[-1]['final']['final'] = {}
cache[-1]['final']['final']['final'] = {}
cache_dic['cache'] = cache
cache_dic['cache_interval'] = cache_interval
cache_dic['max_order'] = max_order
cache_dic['first_enhance'] = first_enhance
cache_dic['end_enhance'] = end_enhance
cache_dic['taylor_cache'] = True
current = {}
current['activated_steps'] = []
current['step'] = 0
current['num_steps'] = num_steps
return cache_dic, current
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