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g rvpljybp jb xwpwcgjw g cgpabm hwcmvjgjybp br g uyzj yp-huglw, gpa g rvpljybp rbc cgpabm zgmhuypx 
nyjqbvj cwhuglwmwpj.

Bp jqw cwgu uypw, jqwcw gcw rvpljybpz jb lbmhvjw vpyrbcm, pbcmgu (Xgvzzygp), ubxpbcmgu, pwxgjyfw 
wdhbpwpjygu, xgmmg, gpa iwjg ayzjcyivjybpz. Rbc xwpwcgjypx ayzjcyivjybpz br gpxuwz, jqw fbp Myzwz 
ayzjcyivjybp yz gfgyugiuw.

Gumbzj guu mbavuw rvpljybpz awhwpa bp jqw igzyl rvpljybp cgpabm(), nqylq xwpwcgjwz g cgpabm rubgj 
vpyrbcmue yp jqw zwmy-bhwp cgpxw [0.0, 1.0). Hejqbp vzwz jqw Mwczwppw Jnyzjwc gz jqw lbcw xwpwcgjbc. 
Yj hcbavlwz 53-iyj hcwlyzybp rubgjz gpa qgz g hwcyba br 2**19937-1. Jqw vpawcueypx ymhuwmwpjgjybp yp 
L yz ibjq rgzj gpa jqcwgazgrw. Jqw Mwczwppw Jnyzjwc yz bpw br jqw mbzj wdjwpzyfwue jwzjwa cgpabm pvmiwc 
xwpwcgjbcz yp wdyzjwplw. Qbnwfwc, iwypx lbmhuwjwue awjwcmypyzjyl, yj yz pbj zvyjgiuw rbc guu hvchbzwz, 
gpa yz lbmhuwjwue 
vpzvyjgiuw rbc lcehjbxcghqyl hvchbzwz.

Jqw rvpljybpz zvhhuywa ie jqyz mbavuw gcw gljvguue ibvpa mwjqbaz br g qyaawp ypzjgplw br jqw 
cgpabm.Cgpabm lugzz. Ebv lgp ypzjgpjygjw ebvc bnp ypzjgplwz br Cgpabm jb xwj xwpwcgjbcz jqgj 
abp'j zqgcw zjgjw. Jqyz yz wzhwlyguue vzwrvu rbc mvujy-jqcwgawa hcbxcgmz, lcwgjypx g ayrrwcwpj 
ypzjgplw br Cgpabm rbc wglq jqcwga, gpa vzypx jqw tvmhgqwga() mwjqba jb mgow yj uyowue jqgj jqw 
xwpwcgjwa zwsvwplwz zwwp ie wglq jqcwga abp'j bfwcugh.

Lugzz Cgpabm lgp guzb iw zvilugzzwa yr ebv ngpj jb vzw g ayrrwcwpj igzyl xwpwcgjbc br ebvc bnp 
awfyzypx: yp jqgj lgzw, bfwccyaw jqw cgpabm(), zwwa(), xwjzjgjw(), zwjzjgjw() gpa tvmhgqwga() mwjqbaz. 
Bhjybpguue, g pwn xwpwcgjbc lgp zvhhue g xwjcgpaiyjz() mwjqba - jqyz guubnz cgpacgpxw() jb hcbavlw 
zwuwljybpz bfwc gp gciyjcgcyue ugcxw cgpxw.

Pwn yp fwczybp 2.4: jqw xwjcgpaiyjz() mwjqba.

Gz gp wdgmhuw br zvilugzzypx, jqw cgpabm mbavuw hcbfyawz jqw NylqmgppQyuu lugzz jqgj ymhuwmwpjz 
gp gujwcpgjyfw xwpwcgjbc yp hvcw Hejqbp. Jqw lugzz hcbfyawz g iglongca lbmhgjyiuw nge jb cwhcbavlw 
cwzvujz rcbm wgcuywc fwczybpz br Hejqbp, nqylq vzwa jqw Nylqmgpp-Qyuu guxbcyjqm gz jqw lbcw xwpwcgjbc. 
Pbjw jqgj jqyz Nylqmgpp-Qyuu xwpwcgjbc lgp pb ubpxwc iw cwlbmmwpawa: yjz hwcyba yz jbb zqbcj ie lbpjwmhbcgce 
zjgpagcaz, gpa jqw zwsvwplw xwpwcgjwa yz opbnp jb rgyu zbmw zjcypxwpj cgpabmpwzz jwzjz. Zww jqw cwrwcwplwz 
iwubn rbc g cwlwpj fgcygpj jqgj cwhgycz jqwzw rugnz.