N400 denied due to lack of continuous residence. Short notice.

help me ASAP !!!!!!!!

I have the same situation as the friend told the story ,

i got LPR on 6, march , 2010 lived in the usa for almost three years, then left USA for my first long visit out of USA on 07/23/2012 and came back 1/1/2013
during this time i got married to non-resident non-citizen of USA , he lives abroad
while i came back looking for a job and couldnt find one , due to my economic situation i decided to leave and since then going back and forth for trips back to back but under 6 months except for one that happened accidentally for 181 days which i believed the 6 months is the rule not the 180 or 181 days
what is the rule anyway ???
i applied for naturalization N400 on my 5th year anniversary dec8, 2015 (90 days earlier ) since i believed i didnt disrupt my residency due to travel under 6months ,
got finger printed on feb, 2015 ,
got interviewed on march30, 2015 ,
Denial letter received on 21 april, 2015 ,

on the interview day , the IO asked to fill out a printed page of 3-4 questions asking of my where about whether i was working abroad , who supported me ??
........... which i clearly said i lost my job and didn't find a job at all , i didn't work abroad just trying to balance the time between USA and with my family (husband)

1)
Do i have a chance to appeal ?? since i want to make a record straight , of any confusing on records they have on file , because i have proof on my trip on 23/7/2012 -1/1/2013 ,
i didn't abandon my job and didn't left my abode in fact i was on leave of absence from work and paying rent even though i was on vacation
Do i really need to do that ??? does that affect my case in future for re-apply ???

2)
The letter doesn't say when i can re-apply how can i find out ???

3)
Does the 4years +1 does apply to my case ??? which date would be in my favor to have on the 364 days rule?? if the trip of 181 days fall in to the 364 would i be denied again ?? should wait longer so the 181 trip wont be in my new 5 year ????
 
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