Problem:


Score : 400 points

Problem Statement

Given is a number sequence A of length N.

Find the number of integers i \left(1 \leq i \leq N\right) with the following property:

For every integer j \left(1 \leq j \leq N\right) such that i \neq j , A_j does not divide A_i.

Constraints

All values in input are integers.

1 \leq N \leq 2 \times 10^5

1 \leq A_i \leq 10^6

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \cdots A_N

Output

Print the answer.

Sample Input 1

5
24 11 8 3 16

Sample Output 1

3

The integers with the property are 2, 3, and 4.

Sample Input 2

4
5 5 5 5

Sample Output 2

0

Note that there can be multiple equal numbers.

Sample Input 3

10
33 18 45 28 8 19 89 86 2 4

Sample Output 3

5



Sample input:
5
24 11 8 3 16


Sample output:
3

Submission status: Time Limit Exceeded

Solution code:
def main():

    P = {142421, 142427, 142433, 142453, 142469, 142501, 142529, 142537, 142543, 142547, 142553, 142559, 142567, 142573, 142589, 142591, 142601, 142607, 142609, 142619, 142657, 142673, 142697, 142699, 142711, 142733, 142757, 142759, 142771, 142787, 142789, 142799, 142811, 142837, 142841, 142867, 142871, 142873, 142897, 142903, 142907, 142939, 142949, 142963, 142969, 142973, 142979, 142981, 142993, 143053, 143063, 143093, 143107, 143111, 143113, 143137, 143141, 143159, 143177, 143197, 143239, 143243, 143249, 143257, 143261, 143263, 143281, 143287, 143291, 143329, 143333, 143357, 143387, 143401, 143413, 143419, 143443, 143461, 143467, 143477, 143483, 143489, 143501, 143503, 143509, 143513, 143519, 143527, 143537, 143551, 143567, 143569, 143573, 143593, 143609, 143617, 143629, 143651, 143653, 143669, 143677, 143687, 143699, 143711, 143719, 143729, 143743, 143779, 143791, 143797, 143807, 143813, 143821, 143827, 143831, 143833, 143873, 143879, 143881, 143909, 143947, 143953, 143971, 143977, 143981, 143999, 144013, 144031, 144037, 144061, 144071, 144073, 144103, 144139, 144161, 144163, 144167, 144169, 144173, 144203, 144223, 144241, 144247, 144253, 144259, 144271, 144289, 144299, 144307, 144311, 144323, 144341, 144349, 144379, 144383, 144407, 144409, 144413, 144427, 144439, 144451, 144461, 144479, 144481, 144497, 144511, 144539, 144541, 144563, 144569, 144577, 144583, 144589, 144593, 144611, 144629, 144659, 144667, 144671, 144701, 144709, 144719, 144731, 144737, 144751, 144757, 144763, 144773, 144779, 144791, 144817, 144829, 144839, 144847, 144883, 144887, 144889, 144899, 144917, 144931, 144941, 144961, 144967, 144973, 144983, 145007, 145009, 145021, 145031, 145037, 145043, 145063, 145069, 145091, 145109, 145121, 145133, 145139, 145177, 145193, 145207, 145213, 145219, 145253, 145259, 145267, 145283, 145289, 145303, 145307, 145349, 145361, 145381, 145391, 145399, 145417, 145423, 145433, 145441, 145451, 145459, 145463, 145471, 145477, 145487, 145501, 145511, 145513, 145517, 145531, 145543, 145547, 145549, 145577, 145589, 145601, 145603, 145633, 145637, 145643, 145661, 145679, 145681, 145687, 145703, 145709, 145721, 145723, 145753, 145757, 145759, 145771, 145777, 145799, 145807, 145819, 145823, 145829, 145861, 145879, 145897, 145903, 145931, 145933, 145949, 145963, 145967, 145969, 145987, 145991, 146009, 146011, 146021, 146023, 146033, 146051, 146057, 146059, 146063, 146077, 146093, 146099, 146117, 146141, 146161, 146173, 146191, 146197, 146203, 146213, 146221, 146239, 146249, 146273, 146291, 146297, 146299, 146309, 146317, 146323, 146347, 146359, 146369, 146381, 146383, 146389, 146407, 146417, 146423, 146437, 146449, 146477, 146513, 146519, 146521, 146527, 146539, 146543, 146563, 146581, 146603, 146609, 146617, 146639, 146647, 146669, 146677, 146681, 146683, 146701, 146719, 146743, 146749, 146767, 146777, 146801, 146807, 146819, 146833, 146837, 146843, 146849, 146857, 146891, 146893, 146917, 146921, 146933, 146941, 146953, 146977, 146983, 146987, 146989, 147011, 147029, 147031, 147047, 147073, 147083, 147089, 147097, 147107, 147137, 147139, 147151, 147163, 147179, 147197, 147209, 147211, 147221, 147227, 147229, 147253, 147263, 147283, 147289, 147293, 147299, 147311, 147319, 147331, 147341, 147347, 147353, 147377, 147391, 147397, 147401, 147409, 147419, 147449, 147451, 147457, 147481, 147487, 147503, 147517, 147541, 147547, 147551, 147557, 147571, 147583, 147607, 147613, 147617, 147629, 147647, 147661, 147671, 147673, 147689, 147703, 147709, 147727, 147739, 147743, 147761, 147769, 147773, 147779, 147787, 147793, 147799, 147811, 147827, 147853, 147859, 147863, 147881, 147919, 147937, 147949, 147977, 147997, 148013, 148021, 148061, 148063, 148073, 148079, 148091, 148123, 148139, 148147, 148151, 148153, 148157, 148171, 148193, 148199, 148201, 148207, 148229, 148243, 148249, 148279, 148301, 148303, 148331, 148339, 148361, 148367, 148381, 148387, 148399, 148403, 148411, 148429, 148439, 148457, 148469, 148471, 148483, 148501, 148513, 148517, 148531, 148537, 148549, 148573, 148579, 148609, 148627, 148633, 148639, 148663, 148667, 148669, 148691, 148693, 148711, 148721, 148723, 148727, 148747, 148763, 148781, 148783, 148793, 148817, 148829, 148853, 148859, 148861, 148867, 148873, 148891, 148913, 148921, 148927, 148931, 148933, 148949, 148957, 148961, 148991, 148997, 149011, 149021, 149027, 149033, 149053, 149057, 149059, 149069, 149077, 149087, 149099, 149101, 149111, 149113, 149119, 149143, 149153, 149159, 149161, 149173, 149183, 149197, 149213, 149239, 149249, 149251, 149257, 149269, 149287, 149297, 149309, 149323, 149333, 149341, 149351, 149371, 149377, 149381, 149393, 149399, 149411, 149417, 149419, 149423, 149441, 149459, 149489, 149491, 149497, 149503, 149519, 149521, 149531, 149533, 149543, 149551, 149561, 149563, 149579, 149603, 149623, 149627, 149629, 149689, 149711, 149713, 149717, 149729, 149731, 149749, 149759, 149767, 149771, 149791, 149803, 149827, 149837, 149839, 149861, 149867, 149873, 149893, 149899, 149909, 149911, 149921, 149939, 149953, 149969, 149971, 149993, 150001, 150011, 150041, 150053, 150061, 150067, 150077, 150083, 150089, 150091, 150097, 150107, 150131, 150151, 150169, 150193, 150197, 150203, 150209, 150211, 150217, 150221, 150223, 150239, 150247, 150287, 150299, 150301, 150323, 150329, 150343, 150373, 150377, 150379, 150383, 150401, 150407, 150413, 150427, 150431, 150439, 150473, 150497, 150503, 150517, 150523, 150533, 150551, 150559, 150571, 150583, 150587, 150589, 150607, 150611, 150617, 150649, 150659, 150697, 150707, 150721, 150743, 150767, 150769, 150779, 150791, 150797, 150827, 150833, 150847, 150869, 150881, 150883, 150889, 150893, 150901, 150907, 150919, 150929, 150959, 150961, 150967, 150979, 150989, 150991, 151007, 151009, 151013, 151027, 151049, 151051, 151057, 151091, 151121, 151141, 151153, 151157, 151163, 151169, 151171, 151189, 151201, 151213, 151237, 151241, 151243, 151247, 151253, 151273, 151279, 151289, 151303, 151337, 151339, 151343, 151357, 151379, 151381, 151391, 151397, 151423, 151429, 151433, 151451, 151471, 151477, 151483, 151499, 151507, 151517, 151523, 151531, 151537, 151549, 151553, 151561, 151573, 151579, 151597, 151603, 151607, 151609, 151631, 151637, 151643, 151651, 151667, 151673, 151681, 151687, 151693, 151703, 151717, 151729, 151733, 151769, 151771, 151783, 151787, 151799, 151813, 151817, 151841, 151847, 151849, 151871, 151883, 151897, 151901, 151903, 151909, 151937, 151939, 151967, 151969, 152003, 152017, 152027, 152029, 152039, 152041, 152063, 152077, 152081, 152083, 152093, 152111, 152123, 152147, 152183, 152189, 152197, 152203, 152213, 152219, 152231, 152239, 152249, 152267, 152287, 152293, 152297, 152311, 152363, 152377, 152381, 152389, 152393, 152407, 152417, 152419, 152423, 152429, 152441, 152443, 152459, 152461, 152501, 152519, 152531, 152533, 152539, 152563, 152567, 152597, 152599, 152617, 152623, 152629, 152639, 152641, 152657, 152671, 152681, 152717, 152723, 152729, 152753, 152767, 152777, 152783, 152791, 152809, 152819, 152821, 152833, 152837, 152839, 152843, 152851, 152857, 152879, 152897, 152899, 152909, 152939, 152941, 152947, 152953, 152959, 152981, 152989, 152993, 153001, 153059, 153067, 153071, 153073, 153077, 153089, 153107, 153113, 153133, 153137, 153151, 153191, 153247, 153259, 153269, 153271, 153277, 153281, 153287, 153313, 153319, 153337, 153343, 153353, 153359, 153371, 153379, 153407, 153409, 153421, 153427, 153437, 153443, 153449, 153457, 153469, 153487, 153499, 153509, 153511, 153521, 153523, 153529, 153533, 153557, 153563, 153589, 153607, 153611, 153623, 153641, 153649, 153689, 153701, 153719, 153733, 153739, 153743, 153749, 153757, 153763, 153817, 153841, 153871, 153877, 153887, 153889, 153911, 153913, 153929, 153941, 153947, 153949, 153953, 153991, 153997, 154001, 154027, 154043, 154057, 154061, 154067, 154073, 154079, 154081, 154087, 154097, 154111, 154127, 154153, 154157, 154159, 154181, 154183, 154211, 154213, 154229, 154243, 154247, 154267, 154277, 154279, 154291, 154303, 154313, 154321, 154333, 154339, 154351, 154369, 154373, 154387, 154409, 154417, 154423, 154439, 154459, 154487, 154493, 154501, 154523, 154543, 154571, 154573, 154579, 154589, 154591, 154613, 154619, 154621, 154643, 154667, 154669, 154681, 154691, 154699, 154723, 154727, 154733, 154747, 154753, 154769, 154787, 154789, 154799, 154807, 154823, 154841, 154849, 154871, 154873, 154877, 154883, 154897, 154927, 154933, 154937, 154943, 154981, 154991, 155003, 155009, 155017, 155027, 155047, 155069, 155081, 155083, 155087, 155119, 155137, 155153, 155161, 155167, 155171, 155191, 155201, 155203, 155209, 155219, 155231, 155251, 155269, 155291, 155299, 155303, 155317, 155327, 155333, 155371, 155377, 155381, 155383, 155387, 155399, 155413, 155423, 155443, 155453, 155461, 155473, 155501, 155509, 155521, 155537, 155539, 155557, 155569, 155579, 155581, 155593, 155599, 155609, 155621, 155627, 155653, 155657, 155663, 155671, 155689, 155693, 155699, 155707, 155717, 155719, 155723, 155731, 155741, 155747, 155773, 155777, 155783, 155797, 155801, 155809, 155821, 155833, 155849, 155851, 155861, 155863, 155887, 155891, 155893, 155921, 156007, 156011, 156019, 156041, 156059, 156061, 156071, 156089, 156109, 156119, 156127, 156131, 156139, 156151, 156157, 156217, 156227, 156229, 156241, 156253, 156257, 156259, 156269, 156307, 156319, 156329, 156347, 156353, 156361, 156371, 156419, 156421, 156437, 156467, 156487, 156491, 156493, 156511, 156521, 156539, 156577, 156589, 156593, 156601, 156619, 156623, 156631, 156641, 156659, 156671, 156677, 156679, 156683, 156691, 156703, 156707, 156719, 156727, 156733, 156749, 156781, 156797, 156799, 156817, 156823, 156833, 156841, 156887, 156899, 156901, 156913, 156941, 156943, 156967, 156971, 156979, 157007, 157013, 157019, 157037, 157049, 157051, 157057, 157061, 157081, 157103, 157109, 157127, 157133, 157141, 157163, 157177, 157181, 157189, 157207, 157211, 157217, 157219, 157229, 157231, 157243, 157247, 157253, 157259, 157271, 157273, 157277, 157279, 157291, 157303, 157307, 157321, 157327, 157349, 157351, 157363, 157393, 157411, 157427, 157429, 157433, 157457, 157477, 157483, 157489, 157513, 157519, 157523, 157543, 157559, 157561, 157571, 157579, 157627, 157637, 157639, 157649, 157667, 157669, 157679, 157721, 157733, 157739, 157747, 157769, 157771, 157793, 157799, 157813, 157823, 157831, 157837, 157841, 157867, 157877, 157889, 157897, 157901, 157907, 157931, 157933, 157951, 157991, 157999, 158003, 158009, 158017, 158029, 158047, 158071, 158077, 158113, 158129, 158141, 158143, 158161, 158189, 158201, 158209, 158227, 158231, 158233, 158243, 158261, 158269, 158293, 158303, 158329, 158341, 158351, 158357, 158359, 158363, 158371, 158393, 158407, 158419, 158429, 158443, 158449, 158489, 158507, 158519, 158527, 158537, 158551, 158563, 158567, 158573, 158581, 158591, 158597, 158611, 158617, 158621, 158633, 158647, 158657, 158663, 158699, 158731, 158747, 158749, 158759, 158761, 158771, 158777, 158791, 158803, 158843, 158849, 158863, 158867, 158881, 158909, 158923, 158927, 158941, 158959, 158981, 158993, 159013, 159017, 159023, 159059, 159073, 159079, 159097, 159113, 159119, 159157, 159161, 159167, 159169, 159179, 159191, 159193, 159199, 159209, 159223, 159227, 159233, 159287, 159293, 159311, 159319, 159337, 159347, 159349, 159361, 159389, 159403, 159407, 159421, 159431, 159437, 159457, 159463, 159469, 159473, 159491, 159499, 159503, 159521, 159539, 159541, 159553, 159563, 159569, 159571, 159589, 159617, 159623, 159629, 159631, 159667, 159671, 159673, 159683, 159697, 159701, 159707, 159721, 159737, 159739, 159763, 159769, 159773, 159779, 159787, 159791, 159793, 159799, 159811, 159833, 159839, 159853, 159857, 159869, 159871, 159899, 159911, 159931, 159937, 159977, 159979, 160001, 160009, 160019, 160031, 160033, 160049, 160073, 160079, 160081, 160087, 160091, 160093, 160117, 160141, 160159, 160163, 160169, 160183, 160201, 160207, 160217, 160231, 160243, 160253, 160309, 160313, 160319, 160343, 160357, 160367, 160373, 160387, 160397, 160403, 160409, 160423, 160441, 160453, 160481, 160483, 160499, 160507, 160541, 160553, 160579, 160583, 160591, 160603, 160619, 160621, 160627, 160637, 160639, 160649, 160651, 160663, 160669, 160681, 160687, 160697, 160709, 160711, 160723, 160739, 160751, 160753, 160757, 160781, 160789, 160807, 160813, 160817, 160829, 160841, 160861, 160877, 160879, 160883, 160903, 160907, 160933, 160967, 160969, 160981, 160997, 161009, 161017, 161033, 161039, 161047, 161053, 161059, 161071, 161087, 161093, 161123, 161137, 161141, 161149, 161159, 161167, 161201, 161221, 161233, 161237, 161263, 161267, 161281, 161303, 161309, 161323, 161333, 161339, 161341, 161363, 161377, 161387, 161407, 161411, 161453, 161459, 161461, 161471, 161503, 161507, 161521, 161527, 161531, 161543, 161561, 161563, 161569, 161573, 161591, 161599, 161611, 161627, 161639, 161641, 161659, 161683, 161717, 161729, 161731, 161741, 161743, 161753, 161761, 161771, 161773, 161779, 161783, 161807, 161831, 161839, 161869, 161873, 161879, 161881, 161911, 161921, 161923, 161947, 161957, 161969, 161971, 161977, 161983, 161999, 162007, 162011, 162017, 162053, 162059, 162079, 162091, 162109, 162119, 162143, 162209, 162221, 162229, 162251, 162257, 162263, 162269, 162277, 162287, 162289, 162293, 162343, 162359, 162389, 162391, 162413, 162419, 162439, 162451, 162457, 162473, 162493, 162499, 162517, 162523, 162527, 162529, 162553, 162557, 162563, 162577, 162593, 162601, 162611, 162623, 162629, 162641, 162649, 162671, 162677, 162683, 162691, 162703, 162709, 162713, 162727, 162731, 162739, 162749, 162751, 162779, 162787, 162791, 162821, 162823, 162829, 162839, 162847, 162853, 162859, 162881, 162889, 162901, 162907, 162917, 162937, 162947, 162971, 162973, 162989, 162997, 163003, 163019, 163021, 163027, 163061, 163063, 163109, 163117, 163127, 163129, 163147, 163151, 163169, 163171, 163181, 163193, 163199, 163211, 163223, 163243, 163249, 163259, 163307, 163309, 163321, 163327, 163337, 163351, 163363, 163367, 163393, 163403, 163409, 163411, 163417, 163433, 163469, 163477, 163481, 163483, 163487, 163517, 163543, 163561, 163567, 163573, 163601, 163613, 163621, 163627, 163633, 163637, 163643, 163661, 163673, 163679, 163697, 163729, 163733, 163741, 163753, 163771, 163781, 163789, 163811, 163819, 163841, 163847, 163853, 163859, 163861, 163871, 163883, 163901, 163909, 163927, 163973, 163979, 163981, 163987, 163991, 163993, 163997, 164011, 164023, 164039, 164051, 164057, 164071, 164089, 164093, 164113, 164117, 164147, 164149, 164173, 164183, 164191, 164201, 164209, 164231, 164233, 164239, 164249, 164251, 164267, 164279, 164291, 164299, 164309, 164321, 164341, 164357, 164363, 164371, 164377, 164387, 164413, 164419, 164429, 164431, 164443, 164447, 164449, 164471, 164477, 164503, 164513, 164531, 164569, 164581, 164587, 164599, 164617, 164621, 164623, 164627, 164653, 164663, 164677, 164683, 164701, 164707, 164729, 164743, 164767, 164771, 164789, 164809, 164821, 164831, 164837, 164839, 164881, 164893, 164911, 164953, 164963, 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    import sys
    input = sys.stdin.buffer.readline
    N = int(input())
    A = [int(i) for i in input().split()]
    A.sort()
    from collections import Counter
    c = Counter(A)
    bl = set()
    for k, v in c.items():
        if v >= 2:
            bl.add(k)
    A = set(A)
    if c[1] == 1:
        return print(1)
    elif c[1] > 1:
        return print(0)

    ans = 0
    for a in A:
        if a in bl:
            continue
        if a in P:
            ans += 1
            continue
        ok = True
        for i in range(2, int(a**0.5)+1):
            if a % i == 0:
                if i in A:
                    ok = False
                if a//i in A:
                    ok = False
            if not ok:
                break
        if ok:
            ans += 1
    print(ans)


if __name__ == '__main__':
    main()