Numerical Palindromes

Let NN be the 15001500-digit string of decimal digits linked here.

Consider all substrings of NN with length strictly greater than 1.1. Let PP be the number of these substrings that are palindromes (read the same forwards and backwards), and let LL be the largest palindromic substring (converted to an integer). Compute the remainder when P+LP + L is divided by 1000.1000.

EDIT: The number is:

  845339512654353013973726529001291079167398839841139949030851696390946980101698124639149591440119733604468880607555560607206064491347909369911515301019367711551352591990261320383329288164577799740443242050242319267457621744807851983932903020081029321152325175250685866007841518940360280269649423980138752509028919270696197406591840726262868909999601238346887569491166411930108771076009573412594100219771074212035289275491573364890832367256854827355325731308226389028814609823679403212837077171147035094962722853937529780881806452156815760851836710785281112178566572142070924792670573967021943625926183861042230278394450084283686782710687142035589512463860007382666540574865786548090984873591052303316826223089810233823833877818493413413377572125316440837829248059997597530413074225936022537356928726861032836482495816729317138037356704312711814039586229918016418907376961773423879993723686730471541871754763457516922397978666764180907493617108196535775671577122375548642715864362660363698285254692252450789495296857844775409285832067120397741225920809730915094640238325092213217491635025536097960140990339793121105117908393671593840606430927286507282838120710540761234699189422511628632095218354056738982111107254470000373451953905544838296347383706816543780729267523585541214385956448406268928721934984154648198940685892036868554606054558448653750977153318569536525693630516086917674823412432181461884413411201293004004992015882876179775802939973661220145456423636324708339384632070192417332964444202
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