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The crystal and electronic structure of an isocyanuric acid derivative was studied by high-resolution single-crystal X-ray diffraction within the Hansen–Coppens multipole formalism. The observed deformation electron density shows signs of thermal smearing. The experimental picture meaningfully assigned to the consequences of unmodelled anharmonic atomic motion. Straightforward simultaneous refinement of all parameters, including Gram–Charlier coefficients, resulted in more significant distortion of apparent static electron density, even though the residual density became significantly flatter and more featureless. Further, the method of transferring multipole parameters from the model refined against theoretical structure factors as an initial guess was employed, followed by the subsequent block refinement of Gram–Charlier coefficients and the other parameters. This procedure allowed us to appropriately distinguish static electron density from the contaminant smearing effects of insufficiently accounted atomic motion. In particular, some covalent bonds and the weak π...π interaction between isocyanurate moieties were studied via the mutual penetration of atomic-like kinetic and electrostatic potential φ-basins with complementary atomic ρ-basins. Further, local electronic temperature was applied as an advanced descriptor for both covalent bonds and noncovalent interactions. Total probability density function (PDF) of nuclear displacement showed virtually no negative regions close to and around the atomic nuclei. The distribution of anharmonic PDF to a certain extent matched the residual electron density from the multipole model before anharmonic refinement. No signs of disordering of the sulfonyl group hidden in the modelled anharmonic motion were found in the PDF.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S2052520621009690/px5043sup1.cif
Contains datablock I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S2052520621009690/px5043Isup2.hkl
Contains datablock I

pdf

Portable Document Format (PDF) file https://doi.org/10.1107/S2052520621009690/px5043sup3.pdf
Tables S1-S3 and Figs. S1-S11

CCDC reference: 2084659

Computing details top

Data collection: APEX3 v2019.11-0 (Bruker AXS); cell refinement: APEX3 v2019.11-0 (Bruker AXS); data reduction: APEX3 v2019.11-0 (Bruker AXS); program(s) used to solve structure: SHELXT-2018/2 (Sheldrick, 2015); program(s) used to refine structure: SHELXL2018/3 (Sheldrick, 2015) for Independent Atom Model refinement; MoPro [version of June 2021] (Jelsch, Guillot et al., 2005) for refinement within the Hansen-Coppens multipole formalism; molecular graphics: MoProViewer v.1.2000 (Jelsch, Guillot et al., 2005); 3DPlot v.2.5.25 (Stash & Tsirelson, 2014); TrajPlot v1.4.0.2 (Stash & Tsirelson, 2014); WinGX v.2021.3 & ORTEP-3 v.2014.1 (Farrugia, 2012); Mercury 2020.3.0 (Macrae, 2020); software used to prepare material for publication: WinXPRO v.3.4.41 (Stash & Tsirelson, 2014); VMoPro [version of June 2021] (Jelsch, Guillot et al., 2005); PLATON [version of June 14th, 2021] (Spek, 2009).

1-{2-[2-(methoxycarbonylmethylsulfonyl)ethoxy]ethyl}-3,5-dimethylisocyanurate top
Crystal data top
C12H19N3O8SDx = 1.544 Mg m3
Mr = 365.36Melting point: 393 K
Monoclinic, P21/cMo Kα radiation, λ = 0.71073 Å
a = 11.2921 (5) ÅCell parameters from 9891 reflections
b = 17.8132 (8) Åθ = 2.2–48.0°
c = 8.3448 (4) ŵ = 0.26 mm1
β = 110.575 (2)°T = 100 K
V = 1571.47 (13) Å3Prism, colorless
Z = 40.31 × 0.30 × 0.22 mm
F(000) = 768
Data collection top
Bruker KAPPA APEX II
diffractometer
19390 independent reflections
Radiation source: sealed x-ray tube, Siemens sealed x-ray tube12487 reflections with I > 3σ(I)
Graphite monochromatorRint = 0.030
ω and φ scansθmax = 55.0°, θmin = 1.9°
Absorption correction: numerical
SADABS-2016/2 (Stalke et al., 2015)
Equivalent reflections defined by point group 2/m for scaling and error model Restraint esd for equal adjacent scale factors = 0.0050 Maximum odd and even orders for spherical harmonics = 1 4 130667 reflections employed for parameter determination Effective data to parameter ratio = 14.14 wR2(int) = 0.0477 (selected reflections only, before parameter refinement) wR2(int) = 0.0436 (selected reflections only, after parameter refinement)
Run 2theta R(int) Incid. factors Diffr. factors K g I/s(lim) Total I>2sig(I) 1 -7.5 0.0220 0.593 - 0.630 0.991 - 1.011 0.797 0.0176 56.7 6018 5350 2 7.5 0.0223 0.593 - 0.614 0.989 - 1.011 0.701 0.0176 56.7 3195 2781 3 47.5 0.0317 0.604 - 0.636 0.985 - 1.011 0.641 0.0176 56.7 20772 16058 4 -10.0 0.0216 0.591 - 0.611 0.991 - 1.011 0.683 0.0176 56.7 1674 1468 5 35.0 0.0293 0.584 - 0.611 0.985 - 1.011 0.663 0.0176 56.7 15219 12134 6 42.5 0.0443 0.564 - 0.627 0.991 - 1.011 0.684 0.0176 56.7 12933 9246 7 35.0 0.0239 0.578 - 0.618 0.994 - 1.011 0.675 0.0176 56.7 8562 7170 8 27.5 0.0240 0.587 - 0.661 0.985 - 1.011 0.663 0.0176 56.7 12387 10378 9 -27.5 0.0243 0.586 - 0.619 0.988 - 1.011 0.713 0.0176 56.7 10333 8724 10 -10.0 0.0256 0.604 - 0.632 0.991 - 1.011 0.687 0.0176 56.7 2582 2251 11 -52.5 0.0336 0.608 - 0.635 0.987 - 1.011 0.639 0.0176 56.7 3692 2871 12 -65.0 0.0483 0.595 - 0.631 0.996 - 1.011 0.752 0.0176 56.7 3126 2116 13 -85.0 0.0855 0.646 - 0.676 0.986 - 1.011 0.660 0.0176 56.7 10184 5134 14 -57.5 0.0345 0.635 - 0.729 0.991 - 1.011 0.731 0.0176 56.7 4790 3555 15 -75.0 0.0565 0.606 - 0.642 0.985 - 1.011 0.619 0.0176 56.7 27040 17030 16 60.0 0.0320 0.611 - 0.657 0.983 - 1.010 0.634 0.0176 56.7 20189 15304 17 75.0 0.0536 0.597 - 0.674 0.984 - 1.010 0.609 0.0176 56.7 20715 13600 18 40.0 0.0356 0.578 - 0.588 1.002 - 1.011 0.671 0.0176 56.7 211 160 19 40.0 0.0430 0.596 - 0.606 0.998 - 1.011 0.659 0.0176 56.7 222 150 20 40.0 0.0458 0.597 - 0.612 1.000 - 1.008 0.794 0.0176 56.7 235 162
Estimated minimum and maximum transmission: 0.8763 0.9074 Additional spherical absorption correction applied with mu*r = 0.0440 Lambda/2 correction factor = 0.00150
h = 2525
Tmin = 0.876, Tmax = 0.907k = 4138
180475 measured reflectionsl = 1718
Refinement top
Refinement on FSecondary atom site location: difference Fourier map
Least-squares matrix: fullHydrogen site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.021Only H-atom coordinates refined
S = 1.39Weighting scheme based on measured s.u.'s weight w was equal to 1/σ2(F1)
12487 reflections(Δ/σ)max = 0.001
150 parametersΔρmax = 0.26 e Å3
0 restraintsΔρmin = 0.30 e Å3
Primary atom site location: structure-invariant direct methods
Special details top

Refinement. The refinement was performed against F1 with the reflections that satisfy the I > 3σ(I) condition. One scale factor was refined. Electroneutrality constraint was imposed on the whole asymmetric cell. The C-H adistances were constrained to the calculated values obtained from the optimized crystal structure. The anisotropic displacement parameters for H-atoms were estimated using the SHADE3 algorithm (Madsen, 2006). Multipole expansion was truncated at the hexadecapole level for the sulfur atom, the octupole level for the other non-hydrogen atoms, and the dipole level for the hydrogen atoms; only the bond- oriented dipoles P10 for all H-atoms were refined. Local symmetry constraints were introduced on multipole parameters. The single κ' parameter was used for all multipoles of each atom. The transfer of multipole parameters from the model refined against theoretical structure factors into the experimental model was performed to reveal the parameters describing the atomic anharmonic motion. A block refinement of the Gram-Charlier coefficients identified by the above- mentioned method and the other parameters led to the final model. No negative values of total electron density were observed. All covalent bonds with non- hydrogen atoms satisfied the rigid bond criterion. Among the all anharmonically refined atoms, no noticeable negative regions of total probability density function of nuclear displacement were observed. More detailed description is in the article.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
S10.464163 (6)0.622306 (1)0.361670 (9)0.013773 (6)
O20.75455 (2)0.45539 (3)1.17134 (5)0.02282 (3)
O40.89848 (2)0.34089 (3)0.78950 (7)0.02430 (3)
O60.86540 (2)0.59448 (2)0.79017 (5)0.01779 (2)
O90.58115 (4)0.623997 (13)0.77436 (6)0.01545 (3)
O10.39821 (2)0.551928 (19)0.33923 (3)0.01678 (3)
O30.439384 (19)0.669640 (17)0.21485 (5)0.01889 (2)
O50.69410 (4)0.72814 (3)0.52276 (3)0.01834 (4)
O140.81018 (4)0.65393 (2)0.41734 (3)0.01499 (3)
N10.80194 (2)0.52647 (2)0.97591 (4)0.01294 (2)
N30.83695 (2)0.39639 (2)0.99264 (5)0.01499 (2)
N50.88746 (2)0.46785 (2)0.79006 (4)0.01369 (2)
C20.79436 (2)0.458983 (17)1.05393 (4)0.01437 (2)
C40.87472 (2)0.397568 (17)0.85258 (4)0.01503 (2)
C60.852002 (19)0.534012 (16)0.84777 (3)0.012197 (19)
C30.83493 (2)0.324510 (19)1.07591 (4)0.02198 (3)
C50.92552 (2)0.470938 (16)0.63973 (4)0.01954 (2)
C70.75037 (3)0.593259 (17)1.03173 (4)0.01634 (2)
C80.60829 (3)0.599906 (15)0.94538 (5)0.01684 (3)
C100.45003 (3)0.633613 (16)0.68675 (5)0.01820 (3)
C110.43048 (2)0.674940 (17)0.52055 (5)0.01678 (3)
C120.62829 (3)0.600377 (16)0.44227 (3)0.01304 (2)
C130.71218 (2)0.668739 (16)0.46629 (3)0.01269 (2)
C150.89649 (3)0.715481 (17)0.43315 (4)0.01992 (3)
H3A0.751 (14)0.3234 (2)1.1112 (4)0.04217
H3B0.8312 (3)0.281 (14)0.9831 (4)0.04309
H3C0.921 (14)0.3192 (2)1.1891 (3)0.04416
H5A1.014 (14)0.44033 (17)0.6672 (5)0.04121
H5B0.8516 (3)0.446 (14)0.5298 (3)0.03718
H5C0.9380 (3)0.530 (14)0.6165 (5)0.03630
H7A0.7745 (4)0.5885 (3)1.169 (14)0.03491
H7B0.7971 (4)0.642 (14)1.0025 (6)0.03160
H8A0.5623 (4)0.546 (14)0.9483 (6)0.03186
H8B0.5748 (4)0.643 (14)1.0151 (5)0.03553
H10A0.4015 (4)0.579 (14)0.6621 (6)0.03237
H10B0.4093 (4)0.669 (14)0.7622 (5)0.03562
H11A0.4866 (4)0.726 (14)0.5426 (6)0.03119
H11B0.330 (14)0.6883 (3)0.4549 (6)0.03500
H12A0.6461 (4)0.573 (14)0.5650 (3)0.02598
H12B0.6408 (4)0.561 (14)0.3499 (4)0.02838
H15A0.8442 (2)0.761 (14)0.3517 (3)0.04009
H15B0.9337 (3)0.73281 (16)0.567 (14)0.03949
H15C0.972 (14)0.69556 (15)0.3914 (4)0.04270
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
S10.01274 (2)0.01191 (2)0.01476 (3)0.001057 (18)0.002454 (18)0.00056 (2)
O20.02926 (15)0.02448 (16)0.01968 (11)0.00214 (9)0.01478 (13)0.00314 (12)
O40.02772 (16)0.01751 (14)0.03040 (15)0.00492 (7)0.01361 (14)0.00140 (12)
O60.02058 (11)0.01630 (12)0.01803 (10)0.00222 (7)0.00870 (12)0.00233 (9)
O90.01556 (13)0.01778 (13)0.01537 (15)0.00045 (7)0.00836 (12)0.00002 (10)
O10.01398 (8)0.01424 (8)0.01887 (14)0.00266 (7)0.00171 (9)0.00043 (8)
O30.01849 (9)0.01783 (9)0.01733 (10)0.00011 (10)0.00253 (9)0.00410 (9)
O50.01890 (11)0.01178 (11)0.02771 (18)0.00262 (10)0.01239 (12)0.00505 (10)
O140.01612 (10)0.01482 (11)0.01645 (14)0.00337 (8)0.00876 (10)0.00350 (9)
N10.01459 (10)0.01377 (10)0.01116 (9)0.00143 (6)0.00540 (9)0.00040 (9)
N30.01338 (10)0.01455 (10)0.01706 (11)0.00127 (7)0.00537 (10)0.00404 (10)
N50.01259 (10)0.01555 (12)0.01409 (10)0.00086 (7)0.00614 (9)0.00076 (10)
C20.01470 (9)0.01605 (10)0.01289 (10)0.00132 (7)0.00548 (8)0.00190 (9)
C40.01301 (9)0.01453 (9)0.01761 (11)0.00180 (7)0.00545 (8)0.00092 (9)
C60.01110 (8)0.01411 (9)0.01118 (9)0.00127 (6)0.00366 (7)0.00046 (8)
C30.02112 (11)0.01771 (10)0.02680 (14)0.00213 (8)0.00802 (10)0.00901 (10)
C50.02095 (10)0.02370 (12)0.01746 (11)0.00284 (8)0.01111 (9)0.00071 (10)
C70.02080 (12)0.01563 (9)0.01358 (11)0.00201 (8)0.00728 (9)0.00353 (10)
C80.02054 (12)0.01681 (11)0.01712 (13)0.00113 (8)0.01156 (10)0.00001 (9)
C100.01548 (11)0.02102 (12)0.02083 (13)0.00059 (8)0.00977 (10)0.00055 (11)
C110.01462 (10)0.01475 (10)0.02107 (14)0.00193 (8)0.00639 (8)0.00000 (11)
C120.01312 (9)0.01095 (9)0.01489 (12)0.00125 (8)0.00470 (7)0.00070 (8)
C130.01345 (8)0.01142 (9)0.01367 (11)0.00169 (7)0.00534 (8)0.00141 (8)
C150.01890 (10)0.01871 (10)0.02556 (14)0.00590 (8)0.01207 (9)0.00406 (10)
H3A0.036980.041280.055570.004210.025380.01542
H3B0.061030.028090.041690.002650.019980.00100
H3C0.035870.045420.039770.000920.000950.01536
H5A0.032280.051000.045580.020420.020190.01029
H5B0.035740.045860.029950.006930.011540.00900
H5C0.048970.024970.043050.001060.026270.00234
H7A0.043690.043140.018780.002630.012070.00066
H7B0.035740.025960.035570.006280.015620.00100
H8A0.033120.028260.036020.004520.014430.00397
H8B0.044650.035550.032540.008900.021240.00565
H10A0.028630.026650.040890.004410.011050.00361
H10B0.038030.037140.039170.012080.022900.00004
H11A0.036370.023210.037090.005840.016790.00314
H11B0.021990.041460.040460.008030.009620.00606
H12A0.026890.029320.021350.002390.008000.00440
H12B0.032500.027060.027220.001930.012560.01089
H15A0.037710.032150.046660.002100.010150.01352
H15B0.044620.043840.029440.017730.012300.00437
H15C0.036610.044450.059330.003040.032170.00088
Geometric parameters (Å, º) top
S1—O31.4316 (4)C3—H3A1.0872
S1—O11.4364 (4)C3—H3C1.0924
S1—C111.7709 (4)C5—H5C1.0877
S1—C121.7787 (3)C5—H5A1.0906
O2—C21.2147 (6)C5—H5B1.0934
O4—C41.2114 (6)C7—C81.5148 (5)
O6—C61.2105 (5)C7—H7A1.0870
O9—C101.4125 (5)C7—H7B1.0871
O9—C81.4168 (6)C8—H8A1.0989
O5—C131.2046 (5)C8—H8B1.1010
O14—C131.3337 (5)C10—C111.5162 (5)
O14—C151.4419 (5)C10—H10A1.0986
N1—C61.3805 (5)C10—H10B1.0993
N1—C21.3841 (5)C11—H11A1.0903
N1—C71.4705 (5)C11—H11B1.0953
N3—C41.3779 (5)C12—C131.5123 (4)
N3—C21.3816 (5)C12—H12A1.0916
N3—C31.4609 (5)C12—H12B1.0932
N5—C41.3830 (5)C15—H15C1.0901
N5—C61.3846 (5)C15—H15A1.0919
N5—C51.4630 (5)C15—H15B1.0923
C3—H3B1.0868
O3—S1—O1117.777 (15)N1—C7—H7A107 (3)
O3—S1—C11107.465 (17)N1—C7—H7B107 (11)
O3—S1—C12108.497 (13)C8—C7—H7A109.8 (7)
O1—S1—C11108.768 (14)C8—C7—H7B110 (1)
O1—S1—C12106.332 (13)H7A—C7—H7B110 (3)
C11—S1—C12107.613 (12)O9—C8—C7108.71 (3)
C10—O9—C8111.99 (3)O9—C8—H8A111 (4)
C13—O14—C15115.38 (3)O9—C8—H8B109 (4)
C6—N1—C2123.97 (3)C7—C8—H8A111 (1)
C6—N1—C7118.83 (3)C7—C8—H8B108 (1)
C2—N1—C7117.18 (3)H8A—C8—H8B110 (14)
C4—N3—C2123.61 (3)O9—C10—C11108.75 (3)
C4—N3—C3118.56 (3)O9—C10—H10A111 (2)
C2—N3—C3117.75 (3)O9—C10—H10B110 (2)
C4—N5—C6123.93 (3)C11—C10—H10A111 (6)
C4—N5—C5117.28 (3)C11—C10—H10B107 (6)
C6—N5—C5118.31 (3)H10A—C10—H10B109 (14)
O2—C2—N3122.12 (4)S1—C11—C10115.29 (2)
O2—C2—N1121.79 (3)S1—C11—H11A108 (7)
N3—C2—N1116.08 (3)S1—C11—H11B101 (4)
O4—C4—N3122.53 (4)C10—C11—H11A111 (6)
O4—C4—N5121.47 (4)C10—C11—H11B111 (1)
N3—C4—N5115.97 (3)H11A—C11—H11B110 (5)
O6—C6—N1122.44 (3)S1—C12—C13113.215 (17)
O6—C6—N5121.84 (3)S1—C12—H12A106 (3)
N1—C6—N5115.71 (3)S1—C12—H12B105 (3)
N3—C3—H3B107 (11)C13—C12—H12A110 (11)
N3—C3—H3A108 (2)C13—C12—H12B113 (10)
N3—C3—H3C109 (2)H12A—C12—H12B110 (10)
H3B—C3—H3A111 (2)O14—C13—O5124.51 (3)
H3B—C3—H3C111 (2)O14—C13—C12110.41 (3)
H3A—C3—H3C111 (9)O5—C13—C12125.09 (3)
N5—C5—H5C106.5 (5)O14—C15—H15C108 (5)
N5—C5—H5A109 (5)O14—C15—H15A108 (10)
N5—C5—H5B109.7 (5)O14—C15—H15B108.2 (9)
H5C—C5—H5A111 (7)H15C—C15—H15A111 (5)
H5C—C5—H5B111 (14)H15C—C15—H15B111 (4)
H5A—C5—H5B110 (8)H15A—C15—H15B111 (5)
N1—C7—C8112.57 (2)
S1—C11—C10—O971.20 (2)N3—C2—N1—C7176.50 (2)
S1—C11—C10—H10A51 (3)N5—C4—N3—C210.02 (2)
S1—C11—C10—H10B170 (3)N5—C4—N3—C3173.49 (2)
S1—C12—C13—O14139.67 (2)N5—C6—N1—C24.56 (2)
S1—C12—C13—O540.85 (3)N5—C6—N1—C7173.92 (2)
O2—C2—N3—C4175.49 (2)C2—N3—C3—H3B156 (2)
O2—C2—N3—C31.02 (2)C2—N3—C3—H3A36 (5)
O2—C2—N1—C6176.77 (2)C2—N3—C3—H3C84 (5)
O2—C2—N1—C74.72 (2)C2—N1—C7—C882.03 (3)
O4—C4—N3—C2171.68 (2)C2—N1—C7—H7A39 (2)
O4—C4—N3—C34.81 (2)C2—N1—C7—H7B156 (2)
O4—C4—N5—C6174.53 (2)C4—N3—C3—H3B21 (2)
O4—C4—N5—C52.61 (2)C4—N3—C3—H3A140 (6)
O6—C6—N1—C2174.76 (2)C4—N3—C3—H3C99 (6)
O6—C6—N1—C76.75 (2)C4—N5—C5—H5C175.4 (3)
O6—C6—N5—C4179.60 (2)C4—N5—C5—H5A56 (6)
O6—C6—N5—C58.56 (2)C4—N5—C5—H5B65.0 (3)
O9—C10—C11—H11A52 (9)C6—N1—C7—C896.56 (2)
O9—C10—C11—H11B174.5 (10)C6—N1—C7—H7A143 (2)
O9—C8—C7—N174.92 (3)C6—N1—C7—H7B25 (2)
O9—C8—C7—H7A166 (1)C6—N5—C5—H5C12 (2)
O9—C8—C7—H7B45 (10)C6—N5—C5—H5A132 (6)
O1—S1—C11—C1050.91 (2)C6—N5—C5—H5B107 (2)
O1—S1—C11—H11A176 (4)C7—C8—O9—C10178.28 (3)
O1—S1—C11—H11B69 (4)C8—O9—C10—C11167.88 (2)
O1—S1—C12—C13177.53 (2)C8—O9—C10—H10A70 (10)
O1—S1—C12—H12A61.7 (6)C8—O9—C10—H10B51 (10)
O1—S1—C12—H12B54.4 (6)C10—O9—C8—H8A60 (10)
O3—S1—C11—C10179.44 (2)C10—O9—C8—H8B61 (10)
O3—S1—C11—H11A56 (3)C10—C11—S1—C1263.90 (3)
O3—S1—C11—H11B60 (6)C11—S1—C12—C1366.06 (3)
O3—S1—C12—C1349.94 (2)C11—S1—C12—H12A55 (9)
O3—S1—C12—H12A171 (8)C11—S1—C12—H12B171 (9)
O3—S1—C12—H12B73 (8)C12—S1—C11—H11A61 (9)
O5—C13—O14—C151.02 (2)C12—S1—C11—H11B176 (2)
O5—C13—C12—H12A78 (4)C12—C13—O14—C15179.49 (2)
O5—C13—C12—H12B159 (4)C13—O14—C15—H15C179 (2)
O14—C13—C12—H12A102 (3)C13—O14—C15—H15A61 (3)
O14—C13—C12—H12B21 (3)C13—O14—C15—H15B59 (4)
N1—C6—N5—C40.27 (2)H7A—C7—C8—H8A72 (11)
N1—C6—N5—C5172.11 (2)H7A—C7—C8—H8B48 (10)
N1—C2—N3—C45.73 (2)H7B—C7—C8—H8A166 (9)
N1—C2—N3—C3177.76 (2)H7B—C7—C8—H8B74 (9)
N1—C7—C8—H8A47 (6)H10A—C10—C11—H11A174 (9)
N1—C7—C8—H8B167 (6)H10A—C10—C11—H11B64 (9)
N3—C4—N5—C67.15 (2)H10B—C10—C11—H11A67 (9)
N3—C4—N5—C5179.07 (2)H10B—C10—C11—H11B55 (9)
N3—C2—N1—C62.01 (2)
 

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