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L1 — Top of Book

Millisecond-resolution best bid/ask analytics.

Top-of-book quote data distilled into interval aggregates: spread, depth, imbalance, mid-price dynamics, and update frequencies — enabling high-resolution microstructure research without raw tick storage.

L1 — Top of Book Datasets

111111111111 _111000_ 100_ _0011_ 11 _0011_ 0 011 _011 _0 0011_ _00 _ _000011 00000111111 ____0000000 ..+ .+cb+. .+ac+ c. .ac. .ac. +b +abc+. bcc++. +aabbbcccc+ ...........111111111110 __111000_ 00_ _0011_ 1 0011_ _0 11_ 001_ 00 _0011 000 _ __000011 0000111111_ 00000000000 ..+ccb +ca+. .+ +ac+ . . .+b+ +b+ +b .+abc+. bc++. aabbccc++++ 000000000000 111000_ _1 0_ _0011_ _ _ _011_ _00 1_ _011 _01 _0011 000 _ _0000111 001111111__ 00000000000 ...++ccbaa+ ba+ .+c +ab+. + +bc. .ac+ .ab .+abc+. c++.. bbccc+++... 000000000___ 0000_ _111 _ _0011_ _0 _0011 _001 1 001_ 001 _0011 000 _ _0000111 0111111___ 00000001111 cccbbaa+.. +. .+ba +ab+. +a .ac. . .ac. .ac .+abc+. c+.. bcc+++... 0_____ 00_ _11100 _0011_ _00 _0011 0011 _ _011 _001 _0011 000 _ _0000111 011111__ 00011111111 baa++.. .+cba. ab+. +ac .ab+ + +b+. .ac .+abc+. c+. cc++... ___11 _111000_ 00011_ _001 0011 0011_ _001_ 0011 _0011 000 _ _0001111 11111__ 11111111111 +.. .+ba+.. c+. +ac+ .+b+. .a .+b+ +ac .+abc+. ++. c++.. ..____11111111 _1111000_ 0111 _0011 011 0011_ 0011 _001_ _0011 000 _ _0001111 11111_ _ 11111111___ . .+cba..+a +. +ac+ +bc. .+b .ac. +bc .+abc+. +.. ++.. .....++++111111110000 110000_ _1 11_ 00011_ 11 0011_ _ _011_ _011_ 0011_ 000 _ _0001111 1111__ __ 11111____ ..+cc .+cba+.+abc +ac+ +ac. +bc +bc. .+bc +abc+. +.. ... .++++aaaabb11100000000_ 000__ _111 1 _00111 1 0011_ _0 0011 _0011 0011_ 000 _ _0001111 111__ __ 111__ ..+ccbaa cba+..+bc+. .+ac+ ac+ .ac+ .+b+. .ab+ .abc+. +. .. +aaabbbbccc0000000__ 0_ __11100 00011_ _0 0011_ _00 011_ _011_ 0011_ 000 _ _0001111 111__ __0 1__ __ .++cbba++. a+..+ab+. .+bc. b+ .ab+ .ac+ .ab+ .abc+. +. . abbbccc+++.00___ __1 _1110000_ _00111 _00 0011_ _001 011 _0011 0011_ 000 _ _0001111 111_ __00 _ ___00 cbba++. ..+ab+. .ab+. . +. .+bc. +bc. .ab+ .+bc+. +. ccc+++.. _ __11111 1111000_ _ 0111_ _0001 0011_ _0011 11_ 0011_ _ _00111 _00 _ _0000111 11__ __00 __00000 a+.. abc+. +ac+. .a . +ac. ab+. +ac+ .+ab+. +. . +++.. 00__ _111 0111_ _000 00011_ _0 _0011 001 011_ _0011_ 11_ _00011 _ _000011 00111111__ 111111___ ..++ccbaa++. +cbaa+..+ab bc+. .a +. .ab+. .+bc. + .abc. .+abc .+aabcc+.. ++aaabbcc++ _ _111100 11_ _00011 _0011_ 000 _0011_ _001 011_ _0011_ 111_ _00011 _ _000011 0011111_ 1111__ _+cbbaa++. ba+..+aabc+ +. .+bc +ab+. +ac+ .+ .abc+ .+abc .+abbc++. +aabbcc++.. __11110000_ _000111_ 0011_ _0011 0011_ _0011 011 _0011_ 111_ _00011 1_ _000011 011111_ 1__ __00baa++. ...+abc+. .+ab+. +ac+. .ab+. .a .abc+ .+abc .+abbc++. aabcc++.. 1110000_ _000111_ _ 11_ _0011_ 011_ _0011_ 11_ 00011_ 111_ _0011 1_ _000011 01111__ _ _ __00000++. +abcc+. .+abc. .+bc+ +bc. .+a .abc+. .+aab .+abbc+.. bbcc+.. 0000__ _00 00111_ 000 1 _00111 11_ _0011_ 11_ _00111_ 011_ _0001 1_ __00011 1111__ _0 __0000011. .+ bc+. .+abc. .abc. ac+ .ab .+bc+. . .+ab .+abcc+. bc++.. 0__ _00001 11_ _00011 _00011_ 0 1_ _00111 11_ _00111 011_ _0001 1_ _00011 1111_ __0 _000011111 .++cb . .+a +abc. +ab+. + b+. .+ac .+bc+. . .+ab .+abcc+. c++. _0001111 _ _000111 00011_ _00 _ _00111 _ 1_ _0011_ 0111_ 0001 11_ _00011 111__ __00 000001111_ ..+cbba+ .++abc c+. +a bc+ .+a c. .abc .+ac+. . .+ab .+abcc+. ++. _0000111_ _000111_ _ 0111 _0001 _00111 _0 1_ _00011_ 0111_ _000 11_ _00001 111_ _000 0001111_ .++cba++.. .+abc+. . +abc +. .+bc + .+ab+ .+abc. +. .+a .+abcc+. +. . 001111_ _0 00111_ _00 11 _00011_ _00111 _00 1 _00011_ 0111_ _000 11_ _00001 111_ _0000 01111_ _0.+ccba+...+a .+abc++. .+abc+. +abc+ . +abc+ .+abc+ +. .+a .+abcc+. . .+ 111_ _0000 11_ _00011 _000111_ 0011_ _000 _ _00111_ 00111_ _000 111_ _0001 11_ _0001 111__ _000ccba+..+aabc abc+. .+abc+. .+ab+. .+ac+. .+abc+ +. .+a .+abcc+. ..+a 1_ _000111 _ _000111_ _000111_ 0 011_ _0001 _ _000111_ 00111_ _00 111_ _0001 11_ _00001 11_ _00001ba+..+abcc+. +. .+ .+bc+. .+abc+. .+abc+. .+abc+ c+. .+ .+abc++. .++ab _ _0001111_ _000111_ 000111_ _0 111_ _0001 1 _000111_ _00111_ _0 0111_ _000 11_ __0001 1_ _000011 .+abc+. +. .+a +abc+. .+abc+. .+abc+. . .+ab abc+. .+abc+. +. .+a _000111_ _ 00111_ _00 111_ _0001 1_ _000111 _000111_ 000111_ _0 0111_ _000 11_ _00011 _ _000111_ .+abc+. .+abc+ c+. .+ .+abc+. .+abc+. . .+ab abc+. .+abc+. .+abc_000111_ _00 111_ _0001 1_ _000111 _ _000111_ _000111_ 0000111_ _ 00111_ _00 111_ 00011 _ _00011_ +abc+. .+abc+. . .+aa +abc+. .+abc+. +. .+a +abc+. .+abc+. .+abc+00111_ _001 1_ _00111_ __000111_ _000111_ __000111_ 0000111_ _ 00111_ _00 111_ 00011 _00011_ bc+. . .+abc+. .+abcc bbc+. .+abc+. +. .+a +abc+. .+abc+ .+ab+. 011_ _00111 _000111_ 000111_ __ 000111_ _ 0000111__ 0000111_ _ 000111_ _0 111_ _00011 _000111 _ +. +ab abc+. .+abc+.. c+. . .++abc+. +. .+ .+bc+. .+bc+. .abc+. 11_ _00011_ 000111 _00 1111_ _000 0111_ _00 0001111_ _ 0000111_ _ 000111_ _0 111_ _00011 _00111_ _0 .+abc+ +. .+a .++abc+. .. .+ .+abbc+. ++. .+ .+abc+. +abc+. .abc+. _ _00111 _ 111_ _0001 1_ _000011 11_ _0000 001111_ __ 0000111_ 000111_ _0 111_ _00011 _00011_ _00 .+abc+. .+abc abc++. .+a ..+abcc+. c+. .+ .+abc+. .+ab+. +abc+ _00011_ _00 1_ _00111_ _0001111_ _ _000011 11111_ _0 0000111__ _000111_ _ 111_ _00011 _0011_ 000 +abc+. .+abc+.. c+. .++ab .+aabc++. c+. . .+abc+. .+ac+. .abc. ._00111 _001 000111_ 0001111_ _ _000001111 111__ _00 00001111_ _000111_ _ 111_ _00011 00111 _001 .+bc+. .+abc+. . .++ ..+abbc .++abbc+.. c+.. . .+bc+. .abc+ abc. .a0011_ _00111 000111_ 00 0111_ _00 000011111_ 11__ _000 00001111_ _000111_ _ 111_ _00011 0011_ _0011 ac+. .+ abc+. ..+aab ..+aabcc+ ..+aabcc+. cc+. . .+ab+. +abc. bc+ +ab011_ _0011_ 0111 _0001 11_ _00001 001111__ __ __0000 00001111_ _000111_ _ 111_ _00111 011_ 00111 c. .+bc c+. .+ .+aabcc+ .++aabcc++. .++abbc++. bc+. .+abc. .+ac+. . c+ +ac+ 0011_ _001 _ _000111_ _ _000001 000011111__ 11111__ __ _0000111_ 000111_ _00 00011_ _0 _0011 000bc. .+ac+ .+abc+ c+.. ..+ .. .+aa .+abc+. .+ac+. ac+. +ac 111 _00111 _000111_ __00001111 0011111__ 11111_ _0 _0000111_ _00111_ _00 _0011_ 00 _0011 0011+. .abc. .+ab+. . ..+ .++aa ..+ .+aa .+abc+. .+ac+. bc. .ab+ 1_ _00111_ 00111_ _00 000011111_ 11111__ 1111__ __0 __000111_ _00111_ _00 _0011_ _00 0011_ _011_. +ab+. .+ac+. .+abb .++aabbc ..++ .++a .+abc+. .+bc+ b+. .+bc. _0011_ _0 111_ _0001 011111_ 11__ __ 111__ __0 __0001111_ _00111_ _00 _0011 001 011_ _001_ +ac+ +ac+. .+aabc++ ..+aabbcc++ ..++aa .++a .+abc+ .+bc+ c. .ac+ _0011_ 000 _ _0000111 111__ __0 _ __000 11__ __00 _0000111_ _00111_ _00 0011_ _001 01_ _0011 _ +bc. . b+. .+a ..+abcc+.. aabbcc++.. ...+++aab ..+a .+abc+. .abc. . +. .+b+. 0011_ _0011 _0001111_ __ __0000 __000000 ___ __00 _0000111_ _00111_ _00 _0011_ _001 11 _0011 _0 +bc. +a . .+abc abbc+.. bcc++.. ..+++aaabbb ..+a .+abc+. .ab+. . . +ac. 11_ _00111 000111__ _ __0000011 __000000001 _ ___00 _0000111_ _00111 _00 _0011 0011 1_ 0011 00 +bc. +bc .+abc+. cc+. ++.. +++aaabbbcc ..+a .+abc+. +ab+. + . .+b+ 1_ _0011_ _ 0111_ _00 _0000011111 00000001111 ___000 _0000111_ _00111 _00 _011_ _0011 _ _011_ 001+bc. .+b+. +abc+. .. . . aaabbbcccc+ ..+a .+abc+. +ac+ + +ac. 00111 00 11_ _00001 000111111__ 00011111111 ___0000 __000111_ _0011_ 000 0011_ _011_ _001_ _011ac. .ab+. .abc+. .++ bbbcccc++++ ..+a .+abc+. .+bc. .+ .+b+ _0011_ _001 _ _0000111 011111__ 111111111__ _____00000 __000111_ _0011_ _001 0011 0011 0011 _011_c. .ab+ +ac+. ..+aab ...+ ccc+++++... ..+a .+abc+. .abc. .a +ac. . 0011 00011 _0000111__ 111__ __ 1111____ _____0000000 __000111_ 00011_ _001 011_ _001_ _011_ 001_ . .ab+ b+. .+ .++abbcc ..+++aa ++....... ..+a .+abc+ +ab+. +a .+b+ + 011 001_ _0 000111_ _ __000011111 00011111111 _________ 000111111_ _00011_ _ 1_ _0011 _0 0011 _001_ ac. .+bc c+. . ccc++++.... abcc+. .+bc. . +. .+b+. c. +ac. 01_ 001_ _01 00111_ _00 000011111__ 1111111___ __000000000 001111111_ _00111_ _ _ 0011_ _0 001_ 0011 _ c. +ab+. . .+ .. ++.... abcc+. .ab+. . + .ac+ + .ac. 1_ 001_ _011 011_ _0001 0011111__ 1111__ 00000000000 001111111_ _00111 _ _ _0011 00 011 _001_ 0 . .+bc+ .++a ..++ . abcc+. .+ac+. + . +bc. . +b+ .

L1 Price

Tier 2

Best bid and ask prices with quantities, midprice, quantity-weighted midprice, time/volume-weighted averages, and quote update frequency.

Key fields

Mid PriceWeighted Mid PriceBid Price TWAPAsk Price VWAP
111111111111 _111000_ 100_ _0011_ 11 _0011_ 0 011 _011 _0 0011_ _00 _ _000011 00000111111 ____0000000 ..+ .+cb+. .+ac+ c. .ac. .ac. +b +abc+. bcc++. +aabbbcccc+ ...........111111111110 __111000_ 00_ _0011_ 1 0011_ _0 11_ 001_ 00 _0011 000 _ __000011 0000111111_ 00000000000 ..+ccb +ca+. .+ +ac+ . . .+b+ +b+ +b .+abc+. bc++. aabbccc++++ 000000000000 111000_ _1 0_ _0011_ _ _ _011_ _00 1_ _011 _01 _0011 000 _ _0000111 001111111__ 00000000000 ...++ccbaa+ ba+ .+c +ab+. + +bc. .ac+ .ab .+abc+. c++.. bbccc+++... 000000000___ 0000_ _111 _ _0011_ _0 _0011 _001 1 001_ 001 _0011 000 _ _0000111 0111111___ 00000001111 cccbbaa+.. +. .+ba +ab+. +a .ac. . .ac. .ac .+abc+. c+.. bcc+++... 0_____ 00_ _11100 _0011_ _00 _0011 0011 _ _011 _001 _0011 000 _ _0000111 011111__ 00011111111 baa++.. .+cba. ab+. +ac .ab+ + +b+. .ac .+abc+. c+. cc++... ___11 _111000_ 00011_ _001 0011 0011_ _001_ 0011 _0011 000 _ _0001111 11111__ 11111111111 +.. .+ba+.. c+. +ac+ .+b+. .a .+b+ +ac .+abc+. ++. c++.. ..____11111111 _1111000_ 0111 _0011 011 0011_ 0011 _001_ _0011 000 _ _0001111 11111_ _ 11111111___ . .+cba..+a +. +ac+ +bc. .+b .ac. +bc .+abc+. +.. ++.. .....++++111111110000 110000_ _1 11_ 00011_ 11 0011_ _ _011_ _011_ 0011_ 000 _ _0001111 1111__ __ 11111____ ..+cc .+cba+.+abc +ac+ +ac. +bc +bc. .+bc +abc+. +.. ... .++++aaaabb11100000000_ 000__ _111 1 _00111 1 0011_ _0 0011 _0011 0011_ 000 _ _0001111 111__ __ 111__ ..+ccbaa cba+..+bc+. .+ac+ ac+ .ac+ .+b+. .ab+ .abc+. +. .. +aaabbbbccc0000000__ 0_ __11100 00011_ _0 0011_ _00 011_ _011_ 0011_ 000 _ _0001111 111__ __0 1__ __ .++cbba++. a+..+ab+. .+bc. b+ .ab+ .ac+ .ab+ .abc+. +. . abbbccc+++.00___ __1 _1110000_ _00111 _00 0011_ _001 011 _0011 0011_ 000 _ _0001111 111_ __00 _ ___00 cbba++. ..+ab+. .ab+. . +. .+bc. +bc. .ab+ .+bc+. +. ccc+++.. _ __11111 1111000_ _ 0111_ _0001 0011_ _0011 11_ 0011_ _ _00111 _00 _ _0000111 11__ __00 __00000 a+.. abc+. +ac+. .a . +ac. ab+. +ac+ .+ab+. +. . +++.. 00__ _111 0111_ _000 00011_ _0 _0011 001 011_ _0011_ 11_ _00011 _ _000011 00111111__ 111111___ ..++ccbaa++. +cbaa+..+ab bc+. .a +. .ab+. .+bc. + .abc. .+abc .+aabcc+.. ++aaabbcc++ _ _111100 11_ _00011 _0011_ 000 _0011_ _001 011_ _0011_ 111_ _00011 _ _000011 0011111_ 1111__ _+cbbaa++. ba+..+aabc+ +. .+bc +ab+. +ac+ .+ .abc+ .+abc .+abbc++. +aabbcc++.. __11110000_ _000111_ 0011_ _0011 0011_ _0011 011 _0011_ 111_ _00011 1_ _000011 011111_ 1__ __00baa++. ...+abc+. .+ab+. +ac+. .ab+. .a .abc+ .+abc .+abbc++. aabcc++.. 1110000_ _000111_ _ 11_ _0011_ 011_ _0011_ 11_ 00011_ 111_ _0011 1_ _000011 01111__ _ _ __00000++. +abcc+. .+abc. .+bc+ +bc. .+a .abc+. .+aab .+abbc+.. bbcc+.. 0000__ _00 00111_ 000 1 _00111 11_ _0011_ 11_ _00111_ 011_ _0001 1_ __00011 1111__ _0 __0000011. .+ bc+. .+abc. .abc. ac+ .ab .+bc+. . .+ab .+abcc+. bc++.. 0__ _00001 11_ _00011 _00011_ 0 1_ _00111 11_ _00111 011_ _0001 1_ _00011 1111_ __0 _000011111 .++cb . .+a +abc. +ab+. + b+. .+ac .+bc+. . .+ab .+abcc+. c++. _0001111 _ _000111 00011_ _00 _ _00111 _ 1_ _0011_ 0111_ 0001 11_ _00011 111__ __00 000001111_ ..+cbba+ .++abc c+. +a bc+ .+a c. .abc .+ac+. . .+ab .+abcc+. ++. _0000111_ _000111_ _ 0111 _0001 _00111 _0 1_ _00011_ 0111_ _000 11_ _00001 111_ _000 0001111_ .++cba++.. .+abc+. . +abc +. .+bc + .+ab+ .+abc. +. .+a .+abcc+. +. . 001111_ _0 00111_ _00 11 _00011_ _00111 _00 1 _00011_ 0111_ _000 11_ _00001 111_ _0000 01111_ _0.+ccba+...+a .+abc++. .+abc+. +abc+ . +abc+ .+abc+ +. .+a .+abcc+. . .+ 111_ _0000 11_ _00011 _000111_ 0011_ _000 _ _00111_ 00111_ _000 111_ _0001 11_ _0001 111__ _000ccba+..+aabc abc+. .+abc+. .+ab+. .+ac+. .+abc+ +. .+a .+abcc+. ..+a 1_ _000111 _ _000111_ _000111_ 0 011_ _0001 _ _000111_ 00111_ _00 111_ _0001 11_ _00001 11_ _00001ba+..+abcc+. +. .+ .+bc+. .+abc+. .+abc+. .+abc+ c+. .+ .+abc++. .++ab _ _0001111_ _000111_ 000111_ _0 111_ _0001 1 _000111_ _00111_ _0 0111_ _000 11_ __0001 1_ _000011 .+abc+. +. .+a +abc+. .+abc+. .+abc+. . .+ab abc+. .+abc+. +. .+a _000111_ _ 00111_ _00 111_ _0001 1_ _000111 _000111_ 000111_ _0 0111_ _000 11_ _00011 _ _000111_ .+abc+. .+abc+ c+. .+ .+abc+. .+abc+. . .+ab abc+. .+abc+. .+abc_000111_ _00 111_ _0001 1_ _000111 _ _000111_ _000111_ 0000111_ _ 00111_ _00 111_ 00011 _ _00011_ +abc+. .+abc+. . .+aa +abc+. .+abc+. +. .+a +abc+. .+abc+. .+abc+00111_ _001 1_ _00111_ __000111_ _000111_ __000111_ 0000111_ _ 00111_ _00 111_ 00011 _00011_ bc+. . .+abc+. .+abcc bbc+. .+abc+. +. .+a +abc+. .+abc+ .+ab+. 011_ _00111 _000111_ 000111_ __ 000111_ _ 0000111__ 0000111_ _ 000111_ _0 111_ _00011 _000111 _ +. +ab abc+. .+abc+.. c+. . .++abc+. +. .+ .+bc+. .+bc+. .abc+. 11_ _00011_ 000111 _00 1111_ _000 0111_ _00 0001111_ _ 0000111_ _ 000111_ _0 111_ _00011 _00111_ _0 .+abc+ +. .+a .++abc+. .. .+ .+abbc+. ++. .+ .+abc+. +abc+. .abc+. _ _00111 _ 111_ _0001 1_ _000011 11_ _0000 001111_ __ 0000111_ 000111_ _0 111_ _00011 _00011_ _00 .+abc+. .+abc abc++. .+a ..+abcc+. c+. .+ .+abc+. .+ab+. +abc+ _00011_ _00 1_ _00111_ _0001111_ _ _000011 11111_ _0 0000111__ _000111_ _ 111_ _00011 _0011_ 000 +abc+. .+abc+.. c+. .++ab .+aabc++. c+. . .+abc+. .+ac+. .abc. ._00111 _001 000111_ 0001111_ _ _000001111 111__ _00 00001111_ _000111_ _ 111_ _00011 00111 _001 .+bc+. .+abc+. . .++ ..+abbc .++abbc+.. c+.. . .+bc+. .abc+ abc. .a0011_ _00111 000111_ 00 0111_ _00 000011111_ 11__ _000 00001111_ _000111_ _ 111_ _00011 0011_ _0011 ac+. .+ abc+. ..+aab ..+aabcc+ ..+aabcc+. cc+. . .+ab+. +abc. bc+ +ab011_ _0011_ 0111 _0001 11_ _00001 001111__ __ __0000 00001111_ _000111_ _ 111_ _00111 011_ 00111 c. .+bc c+. .+ .+aabcc+ .++aabcc++. .++abbc++. bc+. .+abc. .+ac+. . c+ +ac+ 0011_ _001 _ _000111_ _ _000001 000011111__ 11111__ __ _0000111_ 000111_ _00 00011_ _0 _0011 000bc. .+ac+ .+abc+ c+.. ..+ .. .+aa .+abc+. .+ac+. ac+. +ac 111 _00111 _000111_ __00001111 0011111__ 11111_ _0 _0000111_ _00111_ _00 _0011_ 00 _0011 0011+. .abc. .+ab+. . ..+ .++aa ..+ .+aa .+abc+. .+ac+. bc. .ab+ 1_ _00111_ 00111_ _00 000011111_ 11111__ 1111__ __0 __000111_ _00111_ _00 _0011_ _00 0011_ _011_. +ab+. .+ac+. .+abb .++aabbc ..++ .++a .+abc+. .+bc+ b+. .+bc. _0011_ _0 111_ _0001 011111_ 11__ __ 111__ __0 __0001111_ _00111_ _00 _0011 001 011_ _001_ +ac+ +ac+. .+aabc++ ..+aabbcc++ ..++aa .++a .+abc+ .+bc+ c. .ac+ _0011_ 000 _ _0000111 111__ __0 _ __000 11__ __00 _0000111_ _00111_ _00 0011_ _001 01_ _0011 _ +bc. . b+. .+a ..+abcc+.. aabbcc++.. ...+++aab ..+a .+abc+. .abc. . +. .+b+. 0011_ _0011 _0001111_ __ __0000 __000000 ___ __00 _0000111_ _00111_ _00 _0011_ _001 11 _0011 _0 +bc. +a . .+abc abbc+.. bcc++.. ..+++aaabbb ..+a .+abc+. .ab+. . . +ac. 11_ _00111 000111__ _ __0000011 __000000001 _ ___00 _0000111_ _00111 _00 _0011 0011 1_ 0011 00 +bc. +bc .+abc+. cc+. ++.. +++aaabbbcc ..+a .+abc+. +ab+. + . .+b+ 1_ _0011_ _ 0111_ _00 _0000011111 00000001111 ___000 _0000111_ _00111 _00 _011_ _0011 _ _011_ 001+bc. .+b+. +abc+. .. . . aaabbbcccc+ ..+a .+abc+. +ac+ + +ac. 00111 00 11_ _00001 000111111__ 00011111111 ___0000 __000111_ _0011_ 000 0011_ _011_ _001_ _011ac. .ab+. .abc+. .++ bbbcccc++++ ..+a .+abc+. .+bc. .+ .+b+ _0011_ _001 _ _0000111 011111__ 111111111__ _____00000 __000111_ _0011_ _001 0011 0011 0011 _011_c. .ab+ +ac+. ..+aab ...+ ccc+++++... ..+a .+abc+. .abc. .a +ac. . 0011 00011 _0000111__ 111__ __ 1111____ _____0000000 __000111_ 00011_ _001 011_ _001_ _011_ 001_ . .ab+ b+. .+ .++abbcc ..+++aa ++....... ..+a .+abc+ +ab+. +a .+b+ + 011 001_ _0 000111_ _ __000011111 00011111111 _________ 000111111_ _00011_ _ 1_ _0011 _0 0011 _001_ ac. .+bc c+. . ccc++++.... abcc+. .+bc. . +. .+b+. c. +ac. 01_ 001_ _01 00111_ _00 000011111__ 1111111___ __000000000 001111111_ _00111_ _ _ 0011_ _0 001_ 0011 _ c. +ab+. . .+ .. ++.... abcc+. .ab+. . + .ac+ + .ac. 1_ 001_ _011 011_ _0001 0011111__ 1111__ 00000000000 001111111_ _00111 _ _ _0011 00 011 _001_ 0 . .+bc+ .++a ..++ . abcc+. .+ac+. + . +bc. . +b+ .

L1 Imbalance

Tier 3

Bid/ask imbalance, ratio, percentages — both instantaneous (last) and averaged over the interval.

Key fields

ImbalanceImbalance RatioBid/Ask RatioAvg Imbalance
111111111111 _111000_ 100_ _0011_ 11 _0011_ 0 011 _011 _0 0011_ _00 _ _000011 00000111111 ____0000000 ..+ .+cb+. .+ac+ c. .ac. .ac. +b +abc+. bcc++. +aabbbcccc+ ...........111111111110 __111000_ 00_ _0011_ 1 0011_ _0 11_ 001_ 00 _0011 000 _ __000011 0000111111_ 00000000000 ..+ccb +ca+. .+ +ac+ . . .+b+ +b+ +b .+abc+. bc++. aabbccc++++ 000000000000 111000_ _1 0_ _0011_ _ _ _011_ _00 1_ _011 _01 _0011 000 _ _0000111 001111111__ 00000000000 ...++ccbaa+ ba+ .+c +ab+. + +bc. .ac+ .ab .+abc+. c++.. bbccc+++... 000000000___ 0000_ _111 _ _0011_ _0 _0011 _001 1 001_ 001 _0011 000 _ _0000111 0111111___ 00000001111 cccbbaa+.. +. .+ba +ab+. +a .ac. . .ac. .ac .+abc+. c+.. bcc+++... 0_____ 00_ _11100 _0011_ _00 _0011 0011 _ _011 _001 _0011 000 _ _0000111 011111__ 00011111111 baa++.. .+cba. ab+. +ac .ab+ + +b+. .ac .+abc+. c+. cc++... ___11 _111000_ 00011_ _001 0011 0011_ _001_ 0011 _0011 000 _ _0001111 11111__ 11111111111 +.. .+ba+.. c+. +ac+ .+b+. .a .+b+ +ac .+abc+. ++. c++.. ..____11111111 _1111000_ 0111 _0011 011 0011_ 0011 _001_ _0011 000 _ _0001111 11111_ _ 11111111___ . .+cba..+a +. +ac+ +bc. .+b .ac. +bc .+abc+. +.. ++.. .....++++111111110000 110000_ _1 11_ 00011_ 11 0011_ _ _011_ _011_ 0011_ 000 _ _0001111 1111__ __ 11111____ ..+cc .+cba+.+abc +ac+ +ac. +bc +bc. .+bc +abc+. +.. ... .++++aaaabb11100000000_ 000__ _111 1 _00111 1 0011_ _0 0011 _0011 0011_ 000 _ _0001111 111__ __ 111__ ..+ccbaa cba+..+bc+. .+ac+ ac+ .ac+ .+b+. .ab+ .abc+. +. .. +aaabbbbccc0000000__ 0_ __11100 00011_ _0 0011_ _00 011_ _011_ 0011_ 000 _ _0001111 111__ __0 1__ __ .++cbba++. a+..+ab+. .+bc. b+ .ab+ .ac+ .ab+ .abc+. +. . abbbccc+++.00___ __1 _1110000_ _00111 _00 0011_ _001 011 _0011 0011_ 000 _ _0001111 111_ __00 _ ___00 cbba++. ..+ab+. .ab+. . +. .+bc. +bc. .ab+ .+bc+. +. ccc+++.. _ __11111 1111000_ _ 0111_ _0001 0011_ _0011 11_ 0011_ _ _00111 _00 _ _0000111 11__ __00 __00000 a+.. abc+. +ac+. .a . +ac. ab+. +ac+ .+ab+. +. . +++.. 00__ _111 0111_ _000 00011_ _0 _0011 001 011_ _0011_ 11_ _00011 _ _000011 00111111__ 111111___ ..++ccbaa++. +cbaa+..+ab bc+. .a +. .ab+. .+bc. + .abc. .+abc .+aabcc+.. ++aaabbcc++ _ _111100 11_ _00011 _0011_ 000 _0011_ _001 011_ _0011_ 111_ _00011 _ _000011 0011111_ 1111__ _+cbbaa++. ba+..+aabc+ +. .+bc +ab+. +ac+ .+ .abc+ .+abc .+abbc++. +aabbcc++.. __11110000_ _000111_ 0011_ _0011 0011_ _0011 011 _0011_ 111_ _00011 1_ _000011 011111_ 1__ __00baa++. ...+abc+. .+ab+. +ac+. .ab+. .a .abc+ .+abc .+abbc++. aabcc++.. 1110000_ _000111_ _ 11_ _0011_ 011_ _0011_ 11_ 00011_ 111_ _0011 1_ _000011 01111__ _ _ __00000++. +abcc+. .+abc. .+bc+ +bc. .+a .abc+. .+aab .+abbc+.. bbcc+.. 0000__ _00 00111_ 000 1 _00111 11_ _0011_ 11_ _00111_ 011_ _0001 1_ __00011 1111__ _0 __0000011. .+ bc+. .+abc. .abc. ac+ .ab .+bc+. . .+ab .+abcc+. bc++.. 0__ _00001 11_ _00011 _00011_ 0 1_ _00111 11_ _00111 011_ _0001 1_ _00011 1111_ __0 _000011111 .++cb . .+a +abc. +ab+. + b+. .+ac .+bc+. . .+ab .+abcc+. c++. _0001111 _ _000111 00011_ _00 _ _00111 _ 1_ _0011_ 0111_ 0001 11_ _00011 111__ __00 000001111_ ..+cbba+ .++abc c+. +a bc+ .+a c. .abc .+ac+. . .+ab .+abcc+. ++. _0000111_ _000111_ _ 0111 _0001 _00111 _0 1_ _00011_ 0111_ _000 11_ _00001 111_ _000 0001111_ .++cba++.. .+abc+. . +abc +. .+bc + .+ab+ .+abc. +. .+a .+abcc+. +. . 001111_ _0 00111_ _00 11 _00011_ _00111 _00 1 _00011_ 0111_ _000 11_ _00001 111_ _0000 01111_ _0.+ccba+...+a .+abc++. .+abc+. +abc+ . +abc+ .+abc+ +. .+a .+abcc+. . .+ 111_ _0000 11_ _00011 _000111_ 0011_ _000 _ _00111_ 00111_ _000 111_ _0001 11_ _0001 111__ _000ccba+..+aabc abc+. .+abc+. .+ab+. .+ac+. .+abc+ +. .+a .+abcc+. ..+a 1_ _000111 _ _000111_ _000111_ 0 011_ _0001 _ _000111_ 00111_ _00 111_ _0001 11_ _00001 11_ _00001ba+..+abcc+. +. .+ .+bc+. .+abc+. .+abc+. .+abc+ c+. .+ .+abc++. .++ab _ _0001111_ _000111_ 000111_ _0 111_ _0001 1 _000111_ _00111_ _0 0111_ _000 11_ __0001 1_ _000011 .+abc+. +. .+a +abc+. .+abc+. .+abc+. . .+ab abc+. .+abc+. +. .+a _000111_ _ 00111_ _00 111_ _0001 1_ _000111 _000111_ 000111_ _0 0111_ _000 11_ _00011 _ _000111_ .+abc+. .+abc+ c+. .+ .+abc+. .+abc+. . .+ab abc+. .+abc+. .+abc_000111_ _00 111_ _0001 1_ _000111 _ _000111_ _000111_ 0000111_ _ 00111_ _00 111_ 00011 _ _00011_ +abc+. .+abc+. . .+aa +abc+. .+abc+. +. .+a +abc+. .+abc+. .+abc+00111_ _001 1_ _00111_ __000111_ _000111_ __000111_ 0000111_ _ 00111_ _00 111_ 00011 _00011_ bc+. . .+abc+. .+abcc bbc+. .+abc+. +. .+a +abc+. .+abc+ .+ab+. 011_ _00111 _000111_ 000111_ __ 000111_ _ 0000111__ 0000111_ _ 000111_ _0 111_ _00011 _000111 _ +. +ab abc+. .+abc+.. c+. . .++abc+. +. .+ .+bc+. .+bc+. .abc+. 11_ _00011_ 000111 _00 1111_ _000 0111_ _00 0001111_ _ 0000111_ _ 000111_ _0 111_ _00011 _00111_ _0 .+abc+ +. .+a .++abc+. .. .+ .+abbc+. ++. .+ .+abc+. +abc+. .abc+. _ _00111 _ 111_ _0001 1_ _000011 11_ _0000 001111_ __ 0000111_ 000111_ _0 111_ _00011 _00011_ _00 .+abc+. .+abc abc++. .+a ..+abcc+. c+. .+ .+abc+. .+ab+. +abc+ _00011_ _00 1_ _00111_ _0001111_ _ _000011 11111_ _0 0000111__ _000111_ _ 111_ _00011 _0011_ 000 +abc+. .+abc+.. c+. .++ab .+aabc++. c+. . .+abc+. .+ac+. .abc. ._00111 _001 000111_ 0001111_ _ _000001111 111__ _00 00001111_ _000111_ _ 111_ _00011 00111 _001 .+bc+. .+abc+. . .++ ..+abbc .++abbc+.. c+.. . .+bc+. .abc+ abc. .a0011_ _00111 000111_ 00 0111_ _00 000011111_ 11__ _000 00001111_ _000111_ _ 111_ _00011 0011_ _0011 ac+. .+ abc+. ..+aab ..+aabcc+ ..+aabcc+. cc+. . .+ab+. +abc. bc+ +ab011_ _0011_ 0111 _0001 11_ _00001 001111__ __ __0000 00001111_ _000111_ _ 111_ _00111 011_ 00111 c. .+bc c+. .+ .+aabcc+ .++aabcc++. .++abbc++. bc+. .+abc. .+ac+. . c+ +ac+ 0011_ _001 _ _000111_ _ _000001 000011111__ 11111__ __ _0000111_ 000111_ _00 00011_ _0 _0011 000bc. .+ac+ .+abc+ c+.. ..+ .. .+aa .+abc+. .+ac+. ac+. +ac 111 _00111 _000111_ __00001111 0011111__ 11111_ _0 _0000111_ _00111_ _00 _0011_ 00 _0011 0011+. .abc. .+ab+. . ..+ .++aa ..+ .+aa .+abc+. .+ac+. bc. .ab+ 1_ _00111_ 00111_ _00 000011111_ 11111__ 1111__ __0 __000111_ _00111_ _00 _0011_ _00 0011_ _011_. +ab+. .+ac+. .+abb .++aabbc ..++ .++a .+abc+. .+bc+ b+. .+bc. _0011_ _0 111_ _0001 011111_ 11__ __ 111__ __0 __0001111_ _00111_ _00 _0011 001 011_ _001_ +ac+ +ac+. .+aabc++ ..+aabbcc++ ..++aa .++a .+abc+ .+bc+ c. .ac+ _0011_ 000 _ _0000111 111__ __0 _ __000 11__ __00 _0000111_ _00111_ _00 0011_ _001 01_ _0011 _ +bc. . b+. .+a ..+abcc+.. aabbcc++.. ...+++aab ..+a .+abc+. .abc. . +. .+b+. 0011_ _0011 _0001111_ __ __0000 __000000 ___ __00 _0000111_ _00111_ _00 _0011_ _001 11 _0011 _0 +bc. +a . .+abc abbc+.. bcc++.. ..+++aaabbb ..+a .+abc+. .ab+. . . +ac. 11_ _00111 000111__ _ __0000011 __000000001 _ ___00 _0000111_ _00111 _00 _0011 0011 1_ 0011 00 +bc. +bc .+abc+. cc+. ++.. +++aaabbbcc ..+a .+abc+. +ab+. + . .+b+ 1_ _0011_ _ 0111_ _00 _0000011111 00000001111 ___000 _0000111_ _00111 _00 _011_ _0011 _ _011_ 001+bc. .+b+. +abc+. .. . . aaabbbcccc+ ..+a .+abc+. +ac+ + +ac. 00111 00 11_ _00001 000111111__ 00011111111 ___0000 __000111_ _0011_ 000 0011_ _011_ _001_ _011ac. .ab+. .abc+. .++ bbbcccc++++ ..+a .+abc+. .+bc. .+ .+b+ _0011_ _001 _ _0000111 011111__ 111111111__ _____00000 __000111_ _0011_ _001 0011 0011 0011 _011_c. .ab+ +ac+. ..+aab ...+ ccc+++++... ..+a .+abc+. .abc. .a +ac. . 0011 00011 _0000111__ 111__ __ 1111____ _____0000000 __000111_ 00011_ _001 011_ _001_ _011_ 001_ . .ab+ b+. .+ .++abbcc ..+++aa ++....... ..+a .+abc+ +ab+. +a .+b+ + 011 001_ _0 000111_ _ __000011111 00011111111 _________ 000111111_ _00011_ _ 1_ _0011 _0 0011 _001_ ac. .+bc c+. . ccc++++.... abcc+. .+bc. . +. .+b+. c. +ac. 01_ 001_ _01 00111_ _00 000011111__ 1111111___ __000000000 001111111_ _00111_ _ _ 0011_ _0 001_ 0011 _ c. +ab+. . .+ .. ++.... abcc+. .ab+. . + .ac+ + .ac. 1_ 001_ _011 011_ _0001 0011111__ 1111__ 00000000000 001111111_ _00111 _ _ _0011 00 011 _001_ 0 . .+bc+ .++a ..++ . abcc+. .+ac+. + . +bc. . +b+ .

L1 Liquidity

Tier 3

Spread (absolute and bps), depth, dollar depth — instantaneous and interval-averaged.

Key fields

Spread (bps)Total DepthTotal Dollar DepthAvg Spread (bps)

Highlighted Metrics

midprice

Mid Price

Mid Price is the center of the best bid and best ask, making it the cleanest instantaneous fair-value proxy at the top of book.

Because it strips out half-spread noise, it is widely used for microstructure research, marking, and short-horizon return calculations.

weighted_midprice

Weighted Mid Price

Weighted Mid Price tilts the simple midpoint by the relative size resting at the best bid and ask.

That gives it a predictive flavor because it incorporates which side of the top of book is showing more immediate depth.

quote_update_frequency

Quote Update Frequency

Quote Update Frequency measures how actively the top of book was refreshing during the interval.

A high reading often means the market was competitive, reactive, or unstable enough to force frequent repricing.

avg_update_interval

Avg Update Interval

Average Update Interval is the time counterpart to quote frequency, showing how quickly the best quotes changed on average.

Shorter intervals imply a faster and more responsive book, while longer intervals suggest a calmer or less actively managed top of book.

bid_price_vwap

Bid Price VWAP

Bid Price VWAP summarizes where the best bid spent its time with volume-sensitive weighting.

It offers a richer picture than a single snapshot because it reflects how quoted buying interest evolved across the bar.

imbalance

Imbalance

Imbalance measures the raw difference between bid-side and ask-side top-of-book size.

It is one of the fastest ways to see which side is presenting more immediate resting interest at the best quotes.

imbalance_ratio

Imbalance Ratio

Imbalance Ratio scales the raw difference into a relative measure that is easier to compare across symbols and market states.

Because it normalizes for total top-of-book size, it often gives a cleaner signal than the raw imbalance alone.

bid_ask_ratio

Bid/Ask Ratio

Bid/Ask Ratio directly compares the best-bid size with the best-ask size.

It is intuitive, portable, and useful when you want to know whether displayed buying depth materially outweighed displayed selling depth.

bid_percentage_avg

Avg Bid %

Average Bid % shows the mean share of top-level liquidity that sat on the bid across the interval.

This smooths through flicker and highlights the prevailing balance of displayed interest instead of a single instant.

ask_percentage_avg

Avg Ask %

Average Ask % is the complementary view, capturing how much of top-level liquidity tended to sit on the ask side.

Monitoring the bid and ask averages together helps reveal whether one side dominated persistently or whether the book spent the interval near equilibrium.

spread_bps

Spread (bps)

Spread in basis points measures the instantaneous cost of crossing from the best bid to the best ask on a normalized scale.

It is one of the most direct and actionable summaries of top-of-book trading conditions.

spread_depth_ratio

Spread/Depth Ratio

Spread/Depth Ratio combines price width and displayed size into a single liquidity efficiency measure.

A market with tight spreads but little size can still be fragile, and this ratio helps expose that weakness.

total_dollar_depth

Total Dollar Depth

Total Dollar Depth aggregates the top-level bid and ask liquidity in value terms.

This gives a more practical view of executable size than raw units, especially across instruments with different prices.

dollar_depth_bid_avg

Avg Bid Dollar Depth

Average Bid Dollar Depth tracks the mean value resting on the bid at the top of book throughout the interval.

It helps answer whether supportive displayed buying liquidity was consistently present or only flashed briefly.

dollar_depth_ask_avg

Avg Ask Dollar Depth

Average Ask Dollar Depth provides the matching view for displayed sell-side liquidity at the best offer.

Comparing it with the bid average helps reveal whether one side of the book was structurally thinner or thicker during the bar.

Market Microstructure Context

Spread and top-of-book liquidity

BID DEPTHASK DEPTHSPREAD

The spread is the price of immediacy — what the market maker charges to bear adverse selection risk right now. Huang & Stoll (1997) decomposed it into adverse selection, inventory, and order processing costs, which is why a widening spread is diagnostic, not just expensive. But the average hides the regime change: a bar with mean spread of 2 bps that was 0.5 bps for 55 seconds and 8 bps for 5 seconds tells a fundamentally different story than a steady 2 bps. Bollerslev & Melvin (1994) showed spread volatility itself predicts future return volatility — the instability of the spread matters as much as its level.

  • Quoted spread — The gap between best ask and best bid. The sticker price of trading — what you see, not necessarily what you get once real size hits the book.
  • Spread in basis points — Price-normalized spread for cross-asset comparison. A 1-cent spread means something very different on a $10 asset versus a $50,000 one.
  • Top-of-book depth — How much size sits at the best prices. A 1 bps spread on 50k of depth is a different market than 1 bps on 500k. This tells you the cost of the first fill — not whether the market survives the second.
  • Spread/depth ratio — The honesty check on tight spreads. Low ratio means genuinely cheap liquidity. High ratio means the narrow quote is decorative — it will not survive contact with real flow.
Intro to Aperiodic L1 Price Metrics
Interactive notebook

Use Cases

Spread-based execution cost modelling

Use average and instantaneous spread metrics to quantify market-making costs and estimate fill quality across instruments.

Informed trader detection via imbalance

Detect directional pressure from bid/ask imbalance and imbalance ratio dynamics before price moves occur.

Quote update frequency analysis

Identify quote stuffing patterns and measure market-maker activity intensity using update frequency metrics.

VWAP/TWAP quote benchmarking

Compare execution fills against bid/ask VWAP and TWAP to measure adverse selection in your order flow.

High-frequency strategy feature engineering

Use weighted mid-price, imbalance averages, and depth to build predictive features for HFT and MM strategies.

Get started in minutes

curl -fsSL https://raw.githubusercontent.com/aperiodic-io/cli/main/install.sh | bash
github ↗
terminal
# Install the CLI
curl -fsSL https://raw.githubusercontent.com/aperiodic-io/cli/main/install.sh | bash

# Fetch the preview slice as Parquet into ./data — no API key needed
aperiodic flow --preview \
  --exchange binance-futures \
  --symbol perpetual-BTC-USDT:USDT \
  --interval 1h \
  --start-date 2024-01-01 \
  --end-date 2024-01-31 \
  --output-dir ./data
Preview · binance-futures · perpetual-BTC-USDT:USDT · 1h · 2024-01-01 → 2024-01-31
df.head() · 5 × 37
#timetaker_buy_volumetaker_sell_volumetaker_buy_counttaker_sell_countvolume_deltavolume_delta_notionalflow_entropyflow_toxicity_scoretaker_buy_sell_ratiotaker_buy_sell_count_ratiotaker_buy_sell_percentagetaker_buy_sell_count_percentagetaker_buy_small_order_volumetaker_buy_small_order_counttaker_buy_medium_order_volumetaker_buy_medium_order_counttaker_buy_large_order_volumetaker_buy_large_order_counttaker_sell_small_order_volumetaker_sell_small_order_counttaker_sell_medium_order_volumetaker_sell_medium_order_counttaker_sell_large_order_volumetaker_sell_large_order_counttaker_buy_small_order_percentagetaker_buy_medium_order_percentagetaker_buy_large_order_percentagetaker_sell_small_order_percentagetaker_sell_medium_order_percentagetaker_sell_large_order_percentagetaker_buy_small_order_count_percentagetaker_buy_medium_order_count_percentagetaker_buy_large_order_count_percentagetaker_sell_small_order_count_percentagetaker_sell_medium_order_count_percentagetaker_sell_large_order_count_percentage
12024-01-01 00:00:004687.976074218753771.50097656254650041778916.4749755859375388712680.68726718425750731.24300014972686771.11302602291107180.55416858196258540.526745080947876138008.609375268497904352641818910536017398117024.32812518978532792241711515127201571029.4388465881347662088.414062540338.3789062531.0285816192626952262.43920898437540173.05468750.0577204301953315730.56812900304794310.37415054440498350.045406673103570940.5785580873489380.37603524327278137
22024-01-01 01:00:004783.8378906254259.57324218754938640965524.2650146484375223910960.6914658546447754-0.51.12307918071746831.20556569099426270.52898597717285160.5466015934944153140995.4375283810853161283161931864321823277478.26562512409094397236051726176161612029.4732894897460942268.71411132812540383.148437518.1892089843752135.04882812540524.6250.0574656799435615540.57336086034774780.369173437356948850.0302697420120239260.5762236118316650.39350664615631104
32024-01-01 02:00:002141.2590332031252511.808105468752448528065-370.54901123046875-157790900.68997293710708620.94617903232574460.85247713327407840.87243896722793580.4601822495460510.4659371972084045481757.617187515945058392.51306686080624982542772.0781256856032806.5165781009242881080238.1820297241210942362.34497070312540200.937517.028402328491212401.778320312540179.93750.065101079642772670.53363281488418580.401266068220138550.0244076251983642580.59070014953613280.38489222526550293
42024-01-01 03:00:003501.1320800781254618.7480468753615748188-1117.615966796875-474773440.683644711971283-0.170257717370986940.75802618265151980.75033205747604370.431180268526077270.42867982387542725109771.179687521607630267.5201431407325121385478518.9765625125310414373292961854570081763931.3530521392822272179.3715820312540196.289062517.000055313110352254.8041992187540153.089843750.059739470481872560.55709820985794070.383162319660186770.0260023251175880430.60795217752456670.3660454750061035
52024-01-01 04:00:003155.4318847656253201.104003906253664031386-45.672000885009766-1877300.750.69312137365341190.0265556294471025470.985732376575471.1673995256423950.49640744924545290.5386176109313965150556.92187530427435109201351260489201346359707.238281259466590907187841288612721165647.713569641113282356.28881835937539946.6445312518.6520767211914062058.94799804687540255.25781250.083024017512798310.54953604936599730.367439955472946170.0301408264786005020.59848338365554810.37137576937675476

Use with AI Agents

Query L1 — Top of Book datasets programmatically with our Python SDK and REST API — built for autonomous research workflows.

Get Started

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111111111111 _111000_ 100_ _0011_ 11 _0011_ 0 011 _011 _0 0011_ _00 _ _000011 00000111111 ____0000000 ..+ .+cb+. .+ac+ c. .ac. .ac. +b +abc+. bcc++. +aabbbcccc+ ...........111111111110 __111000_ 00_ _0011_ 1 0011_ _0 11_ 001_ 00 _0011 000 _ __000011 0000111111_ 00000000000 ..+ccb +ca+. .+ +ac+ . . .+b+ +b+ +b .+abc+. bc++. aabbccc++++ 000000000000 111000_ _1 0_ _0011_ _ _ _011_ _00 1_ _011 _01 _0011 000 _ _0000111 001111111__ 00000000000 ...++ccbaa+ ba+ .+c +ab+. + +bc. .ac+ .ab .+abc+. c++.. bbccc+++... 000000000___ 0000_ _111 _ _0011_ _0 _0011 _001 1 001_ 001 _0011 000 _ _0000111 0111111___ 00000001111 cccbbaa+.. +. .+ba +ab+. +a .ac. . .ac. .ac .+abc+. c+.. bcc+++... 0_____ 00_ _11100 _0011_ _00 _0011 0011 _ _011 _001 _0011 000 _ _0000111 011111__ 00011111111 baa++.. .+cba. ab+. +ac .ab+ + +b+. .ac .+abc+. c+. cc++... ___11 _111000_ 00011_ _001 0011 0011_ _001_ 0011 _0011 000 _ _0001111 11111__ 11111111111 +.. .+ba+.. c+. +ac+ .+b+. .a .+b+ +ac .+abc+. ++. c++.. ..____11111111 _1111000_ 0111 _0011 011 0011_ 0011 _001_ _0011 000 _ _0001111 11111_ _ 11111111___ . .+cba..+a +. +ac+ +bc. .+b .ac. +bc .+abc+. +.. ++.. .....++++111111110000 110000_ _1 11_ 00011_ 11 0011_ _ _011_ _011_ 0011_ 000 _ _0001111 1111__ __ 11111____ ..+cc .+cba+.+abc +ac+ +ac. +bc +bc. .+bc +abc+. +.. ... .++++aaaabb11100000000_ 000__ _111 1 _00111 1 0011_ _0 0011 _0011 0011_ 000 _ _0001111 111__ __ 111__ ..+ccbaa cba+..+bc+. .+ac+ ac+ .ac+ .+b+. .ab+ .abc+. +. .. +aaabbbbccc0000000__ 0_ __11100 00011_ _0 0011_ _00 011_ _011_ 0011_ 000 _ _0001111 111__ __0 1__ __ .++cbba++. a+..+ab+. .+bc. b+ .ab+ .ac+ .ab+ .abc+. +. . abbbccc+++.00___ __1 _1110000_ _00111 _00 0011_ _001 011 _0011 0011_ 000 _ _0001111 111_ __00 _ ___00 cbba++. ..+ab+. .ab+. . +. .+bc. +bc. .ab+ .+bc+. +. ccc+++.. _ __11111 1111000_ _ 0111_ _0001 0011_ _0011 11_ 0011_ _ _00111 _00 _ _0000111 11__ __00 __00000 a+.. abc+. +ac+. .a . +ac. ab+. +ac+ .+ab+. +. . +++.. 00__ _111 0111_ _000 00011_ _0 _0011 001 011_ _0011_ 11_ _00011 _ _000011 00111111__ 111111___ ..++ccbaa++. +cbaa+..+ab bc+. .a +. .ab+. .+bc. + .abc. .+abc .+aabcc+.. ++aaabbcc++ _ _111100 11_ _00011 _0011_ 000 _0011_ _001 011_ _0011_ 111_ _00011 _ _000011 0011111_ 1111__ _+cbbaa++. ba+..+aabc+ +. .+bc +ab+. +ac+ .+ .abc+ .+abc .+abbc++. +aabbcc++.. __11110000_ _000111_ 0011_ _0011 0011_ _0011 011 _0011_ 111_ _00011 1_ _000011 011111_ 1__ __00baa++. ...+abc+. .+ab+. +ac+. .ab+. .a .abc+ .+abc .+abbc++. aabcc++.. 1110000_ _000111_ _ 11_ _0011_ 011_ _0011_ 11_ 00011_ 111_ _0011 1_ _000011 01111__ _ _ __00000++. +abcc+. .+abc. .+bc+ +bc. .+a .abc+. .+aab .+abbc+.. bbcc+.. 0000__ _00 00111_ 000 1 _00111 11_ _0011_ 11_ _00111_ 011_ _0001 1_ __00011 1111__ _0 __0000011. .+ bc+. .+abc. .abc. ac+ .ab .+bc+. . .+ab .+abcc+. bc++.. 0__ _00001 11_ _00011 _00011_ 0 1_ _00111 11_ _00111 011_ _0001 1_ _00011 1111_ __0 _000011111 .++cb . .+a +abc. +ab+. + b+. .+ac .+bc+. . .+ab .+abcc+. c++. _0001111 _ _000111 00011_ _00 _ _00111 _ 1_ _0011_ 0111_ 0001 11_ _00011 111__ __00 000001111_ ..+cbba+ .++abc c+. +a bc+ .+a c. .abc .+ac+. . .+ab .+abcc+. ++. _0000111_ _000111_ _ 0111 _0001 _00111 _0 1_ _00011_ 0111_ _000 11_ _00001 111_ _000 0001111_ .++cba++.. .+abc+. . +abc +. .+bc + .+ab+ .+abc. +. .+a .+abcc+. +. . 001111_ _0 00111_ _00 11 _00011_ _00111 _00 1 _00011_ 0111_ _000 11_ _00001 111_ _0000 01111_ _0.+ccba+...+a .+abc++. .+abc+. +abc+ . +abc+ .+abc+ +. .+a .+abcc+. . .+ 111_ _0000 11_ _00011 _000111_ 0011_ _000 _ _00111_ 00111_ _000 111_ _0001 11_ _0001 111__ _000ccba+..+aabc abc+. .+abc+. .+ab+. .+ac+. .+abc+ +. .+a .+abcc+. ..+a 1_ _000111 _ _000111_ _000111_ 0 011_ _0001 _ _000111_ 00111_ _00 111_ _0001 11_ _00001 11_ _00001ba+..+abcc+. +. .+ .+bc+. .+abc+. .+abc+. .+abc+ c+. .+ .+abc++. .++ab _ _0001111_ _000111_ 000111_ _0 111_ _0001 1 _000111_ _00111_ _0 0111_ _000 11_ __0001 1_ _000011 .+abc+. +. .+a +abc+. .+abc+. .+abc+. . .+ab abc+. .+abc+. +. .+a _000111_ _ 00111_ _00 111_ _0001 1_ _000111 _000111_ 000111_ _0 0111_ _000 11_ _00011 _ _000111_ .+abc+. .+abc+ c+. .+ .+abc+. .+abc+. . .+ab abc+. .+abc+. .+abc_000111_ _00 111_ _0001 1_ _000111 _ _000111_ _000111_ 0000111_ _ 00111_ _00 111_ 00011 _ _00011_ +abc+. .+abc+. . .+aa +abc+. .+abc+. +. .+a +abc+. .+abc+. .+abc+00111_ _001 1_ _00111_ __000111_ _000111_ __000111_ 0000111_ _ 00111_ _00 111_ 00011 _00011_ bc+. . .+abc+. .+abcc bbc+. .+abc+. +. .+a +abc+. .+abc+ .+ab+. 011_ _00111 _000111_ 000111_ __ 000111_ _ 0000111__ 0000111_ _ 000111_ _0 111_ _00011 _000111 _ +. +ab abc+. .+abc+.. c+. . .++abc+. +. .+ .+bc+. .+bc+. .abc+. 11_ _00011_ 000111 _00 1111_ _000 0111_ _00 0001111_ _ 0000111_ _ 000111_ _0 111_ _00011 _00111_ _0 .+abc+ +. .+a .++abc+. .. .+ .+abbc+. ++. .+ .+abc+. +abc+. .abc+. _ _00111 _ 111_ _0001 1_ _000011 11_ _0000 001111_ __ 0000111_ 000111_ _0 111_ _00011 _00011_ _00 .+abc+. .+abc abc++. .+a ..+abcc+. c+. .+ .+abc+. .+ab+. +abc+ _00011_ _00 1_ _00111_ _0001111_ _ _000011 11111_ _0 0000111__ _000111_ _ 111_ _00011 _0011_ 000 +abc+. .+abc+.. c+. .++ab .+aabc++. c+. . .+abc+. .+ac+. .abc. ._00111 _001 000111_ 0001111_ _ _000001111 111__ _00 00001111_ _000111_ _ 111_ _00011 00111 _001 .+bc+. .+abc+. . .++ ..+abbc .++abbc+.. c+.. . .+bc+. .abc+ abc. .a0011_ _00111 000111_ 00 0111_ _00 000011111_ 11__ _000 00001111_ _000111_ _ 111_ _00011 0011_ _0011 ac+. .+ abc+. ..+aab ..+aabcc+ ..+aabcc+. cc+. . .+ab+. +abc. bc+ +ab011_ _0011_ 0111 _0001 11_ _00001 001111__ __ __0000 00001111_ _000111_ _ 111_ _00111 011_ 00111 c. .+bc c+. .+ .+aabcc+ .++aabcc++. .++abbc++. bc+. .+abc. .+ac+. . c+ +ac+ 0011_ _001 _ _000111_ _ _000001 000011111__ 11111__ __ _0000111_ 000111_ _00 00011_ _0 _0011 000bc. .+ac+ .+abc+ c+.. ..+ .. .+aa .+abc+. .+ac+. ac+. +ac 111 _00111 _000111_ __00001111 0011111__ 11111_ _0 _0000111_ _00111_ _00 _0011_ 00 _0011 0011+. .abc. .+ab+. . ..+ .++aa ..+ .+aa .+abc+. .+ac+. bc. .ab+ 1_ _00111_ 00111_ _00 000011111_ 11111__ 1111__ __0 __000111_ _00111_ _00 _0011_ _00 0011_ _011_. +ab+. .+ac+. .+abb .++aabbc ..++ .++a .+abc+. .+bc+ b+. .+bc. _0011_ _0 111_ _0001 011111_ 11__ __ 111__ __0 __0001111_ _00111_ _00 _0011 001 011_ _001_ +ac+ +ac+. .+aabc++ ..+aabbcc++ ..++aa .++a .+abc+ .+bc+ c. .ac+ _0011_ 000 _ _0000111 111__ __0 _ __000 11__ __00 _0000111_ _00111_ _00 0011_ _001 01_ _0011 _ +bc. . b+. .+a ..+abcc+.. aabbcc++.. ...+++aab ..+a .+abc+. .abc. . +. .+b+. 0011_ _0011 _0001111_ __ __0000 __000000 ___ __00 _0000111_ _00111_ _00 _0011_ _001 11 _0011 _0 +bc. +a . .+abc abbc+.. bcc++.. ..+++aaabbb ..+a .+abc+. .ab+. . . +ac. 11_ _00111 000111__ _ __0000011 __000000001 _ ___00 _0000111_ _00111 _00 _0011 0011 1_ 0011 00 +bc. +bc .+abc+. cc+. ++.. +++aaabbbcc ..+a .+abc+. +ab+. + . .+b+ 1_ _0011_ _ 0111_ _00 _0000011111 00000001111 ___000 _0000111_ _00111 _00 _011_ _0011 _ _011_ 001+bc. .+b+. +abc+. .. . . aaabbbcccc+ ..+a .+abc+. +ac+ + +ac. 00111 00 11_ _00001 000111111__ 00011111111 ___0000 __000111_ _0011_ 000 0011_ _011_ _001_ _011ac. .ab+. .abc+. .++ bbbcccc++++ ..+a .+abc+. .+bc. .+ .+b+ _0011_ _001 _ _0000111 011111__ 111111111__ _____00000 __000111_ _0011_ _001 0011 0011 0011 _011_c. .ab+ +ac+. ..+aab ...+ ccc+++++... ..+a .+abc+. .abc. .a +ac. . 0011 00011 _0000111__ 111__ __ 1111____ _____0000000 __000111_ 00011_ _001 011_ _001_ _011_ 001_ . .ab+ b+. .+ .++abbcc ..+++aa ++....... ..+a .+abc+ +ab+. +a .+b+ + 011 001_ _0 000111_ _ __000011111 00011111111 _________ 000111111_ _00011_ _ 1_ _0011 _0 0011 _001_ ac. .+bc c+. . ccc++++.... abcc+. .+bc. . +. .+b+. c. +ac. 01_ 001_ _01 00111_ _00 000011111__ 1111111___ __000000000 001111111_ _00111_ _ _ 0011_ _0 001_ 0011 _ c. +ab+. . .+ .. ++.... abcc+. .ab+. . + .ac+ + .ac. 1_ 001_ _011 011_ _0001 0011111__ 1111__ 00000000000 001111111_ _00111 _ _ _0011 00 011 _001_ 0 . .+bc+ .++a ..++ . abcc+. .+ac+. + . +bc. . +b+ .

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