Holistic processing of faces as measured by the Thatcher illusion is intact in autism spectrum disorders

Abstract

Impaired face perception in autism spectrum disorders is thought to reflect a perceptual style characterized by componential rather than configural processing of faces. This study investigated face processing in adolescents with autism spectrum disorders using the Thatcher illusion, a perceptual phenomenon exhibiting ‘inversion effects’ that characterize typical face processing. While previous studies used a limited range of face orientations, we measured perception of normality/grotesqueness of faces at seven orientations ranging from upright to inverted to allow for a detailed comparison of both reaction time and error by orientation profiles. We found that, like their typically developing peers, adolescents with autism spectrum disorders show strong inversion effects whereby reaction times were longer and error rates greater at inverted when compared to upright orientations. Additionally, the adolescents with autism spectrum disorders, like their peers in the typically developing group, show a marked nonlinearity in the error by orientation profile. Error is roughly constant out to 90° and then increases steeply, indicating a sudden shift from configural to local processing that reflects experience with faces in their typical orientations. These findings agree with recent reports that face perception is qualitatively similar in autistic and neurotypical groups.

Keywords

autism spectrum disorders configural processing face perception inversion effects Thatcher illusion

Introduction

Autism is a neurodevelopmental disorder characterized by impairments in social interaction, language and communication, and by atypical behaviours and interests (American Psychiatric Association (APA), 2006). In addition to these core differences, a range of perceptual anomalies – including in how faces are viewed, processed and recognized – are reported in autism spectrum disorders (ASD). Reviews of early research highlight an atypical perceptual style characterized by piecemeal or feature-based processing of faces (Behrmann et al., 2006; Dawson et al., 2005). Such perceptual impairments may precede and underpin problems in social cognition (Behrmann et al., 2006; Dakin and Frith, 2005). Alternatively, a lack of interest in social stimuli from early infancy may preclude the development of an expert recognition system that is sensitive to facial configuration (Dawson et al., 2005).

As research in this area grows, recent reviews stress that evidence for impaired face perception in ASD is mixed and that the mechanisms underlying reported difficulties in face processing are still poorly understood (Simmons et al., 2009; Weigelt et al., 2012). Weigelt et al. (2012) provide a comprehensive review of the perception of facial identity in ASD that focuses on a question that is central to this study, that is, whether people with ASD process faces in a qualitatively different way to others or whether their impairments are largely quantitative. Faces are a class of visual stimuli with high self-similarity, and it is generally accepted that our expertise in discriminating and identifying them involves an accurate representation of their shape or configuration (Allen et al., 2009; Diamond and Carey, 1986; Maurer et al., 2002). ‘Configuration’ refers both to first-order relations between features – the generic arrangement of the eyes, nose and mouth – and to second-order relations that describe the precise geometric arrangement of the features in a face.

Thus, weak central coherence theory, which posits a processing bias for local information at the expense of configuration in ASD (Frith, 1989; Happé, 1999), provides a useful framework for thinking about anomalous perception of faces. The theory receives support from demonstrations of superior local processing in ASD, as in the embedded figures and the block design tests (Jolliffe and Baron-Cohen, 1997; Shah and Frith, 1993). However, the idea that people with ASD are insensitive to configural information remains controversial, and it has recently been argued that there is little to support the theory in the specific case of face perception (Weigelt et al., 2012).

Face inversion is known to disrupt configural processing, leading to slower response times and increased error rates in various perception, discrimination and recognition tasks (Maurer et al., 2002), so that the manipulation of stimulus orientation is a very useful tool in revealing stimulus-specific configural processing. Weigelt et al. (2012) note the face inversion effect as one of the ‘markers of typical face perception’. In evaluating studies in this area, they note that a statistically significant interaction between group membership (ASD/typically developing) and face orientation (upright/inverted) is necessary to conclude that people with ASD do not show an inversion effect or, alternatively, that they show a reduced inversion effect. By this criterion, few studies provide evidence for a qualitatively different style of face processing in ASD. Specifically, of the four studies that studied the inversion effect directly, only one showed a significant group by orientation interaction, and of the seven studies that studied the inversion effect indirectly (e.g. using the part-whole effect or the Thatcher illusion), only two provide statistical evidence for a reduced or absent inversion effect (Weigelt et al., 2012).

This study asks whether people with ASD are sensitive to configural information in faces using the Thatcher illusion. In this illusion, the eyes and mouth are inverted in an upright face that is automatically and effortlessly perceived as ‘distorted’ or ‘grotesque’, whereas when the doctored stimulus is turned upside down, the distortion is hard if not impossible to detect (Thompson, 1980). The usual explanation for the effect is that configural processing is disrupted by inversion, leaving participants to rely on an analysis of facial features.

To date, only two studies have used the Thatcher illusion to study configural processing in children and adolescents with ASD. Rouse et al. (2004) compared the performance of children with autism (n = 11, mean age ~9 years) to both typically developing children and children with moderate learning difficulties on a 2AFC version of the Thatcher illusion. Two faces, one Thactherized and one normal, were positioned side by side in either upright or inverted orientation, and the children were asked to indicate which one was ‘funny’ or ‘strange’. Although this was not a reaction-timed task, both reaction time (RT) and accuracy were analysed. There was a significant effect of orientation, such that participants were both faster and more accurate in discriminating the upright faces than the inverted faces. But neither the main effect of group nor the group by orientation interaction were significant. The authors conclude that children with autism are as susceptible to the Thatcher illusion as typically developing children, thereby indicating intact configural processing.

Riby et al. (2009) tested children with autism (n = 20, mean age ~15 years) on the Thatcher illusion using the same 2AFC paradigm as Rouse et al. (2004) and faces that were presented at 0°, 90° and 180°. Performance was compared to that of children with Williams syndrome and typically developing children. Accuracy was no different between those with autism and those in the other two groups, and notably, there was no group by orientation interactions, all groups being equally disadvantaged by stimulus inversion.

While these two studies argue for intact configural processing of faces, it is possible that children with ASD show comparable performance to typically developing children while using different processing strategies. In order to address this potential confound, our study differs from these previous studies of the Thatcher illusion in two important ways. First, both studies used a discrimination task – whereby a Thatcherized and normal face are presented side by side on each trial – introduced by Rouse et al. (2004) as being particularly suited to the young children they tested. It is possible that this task encourages the use of local processing strategies, for example, when presented with a pair of faces on each trial participants who favour a ‘local processing’ style, as has been argued in the case of ASD, might quickly compare the orientation of the eyes across the two faces. Judging which face has inverted eyes may be faster and more accurate for upright than for inverted faces. In this study, we use the more conventional method whereby participants see a single face on each trial and have to say, as quickly as possible, whether it is normal or distorted. In using a reaction-timed task, we hoped to tap into the most salient aspect of the Thatcher illusion, that is, when upright, Thatcherized faces are immediately and effortlessly perceived to be grotesque (Thompson, 1980).

However, it could be argued that the single presentation method is also open to this same confound, that is, that participants with a bias towards local processing may focus on the eyes rather than on the whole face during the task. To explore this possibility, our second change to the experimental protocol involved presenting the faces at a range for orientations – sampled in steps of 30° from 0° to 180° (see Figure 1) – so that performance could be profiled across orientation. If using a local strategy, we might expect participants’ performance to deteriorate gradually as the face is rotated away from the upright towards the inverted, for example, if using a strategy whereby they mentally rotate the stimulus to the upright in judging the orientation of the eyes in the face.

Figure 1.

One of the 10 faces is shown in both Thatcherized (top) and original (bottom) form at the seven orientations used in the experiment. Whereas the difference between the two forms is striking for orientations at and close to the upright, it is much less obvious for orientations at and close to the inverted. These images are reproduced with the permission of the model.

Interestingly, this method has been used previously with adult participants to ask whether there is a gradual or more abrupt shift from configural to local processing as a face is rotated away from upright, and, interestingly, the answer to this question seems to depend on which measure of performance is analysed. For example, Stürzel and Spillmann (2000) asked participants to note the point at which Thatcherized faces – rotated gradually between upright and inverted orientations – shifted in appearance from ‘normal’ to ‘grotesque’ and report a switch from configural to local processing that is restricted to a narrow range of orientations between 94° and 100°. In contrast, Lewis (2001) reports a more gradual shift from configural to local processing based on his analysis of how RT changes with face orientation. Finally, analysing the mean ‘bizarreness’ ratings for Thatcherized faces, Murray et al. (2000) report a sharp discontinuity between 90° and 120°. Therefore, analyses that focus on participants’ ratings of grotesqueness – as measured by percent correct or proportion judged to be grotesque – point to an abrupt shift in processing, whereas analyses that focus on RTs suggest a more gradual one.

Collectively, this research supports a view of face processing in which both features and the spatial relations between those features are processed at upright orientations, whereas configural but not featural processing is compromised when faces are inverted. Demonstrating that adolescents with ASD show a similar shift in processing as their neurotypical peers as faces are rotated from the upright to upside down would greatly strengthen the conclusion that configural processing is intact in ASD. To this end, two groups of adolescents, one with ASD and one age-matched typically developing group were tested on their perception of the Thatcher illusion over seven orientations and both error and RT were analysed.

Methods

Participants

Participants for the experimental group were referred to the study by the third author, a professor of Child and Adolescent Psychiatry whose research speciality is autism. Of the 15 initially recruited, one participant who had a co-morbid diagnosis of attention-deficit hyperactivity disorder (ADHD) performed at chance on the experimental task, and their data were excluded. The remaining 14 participants – all male, ranging in age from 11 to 17 years, with a mean age of 13.74 years (standard deviation (SD) = 1.60 years) – were diagnosed on the autism spectrum by the psychiatrist, who has over 25 years of clinical experience in the area of autism, using a structured assessment according to DSM-IV criteria. Participants did not partake in a further research diagnosis using an instrument such as the Autism Diagnostic Observation Schedule (ADOS) (Lord et al., 1994). Research shows high agreement (~75%) between clinical diagnoses and diagnoses based on instruments such as the ADOS with inconsistencies largely reflecting false positives made by the research instruments (Mazefsky and Oswald, 2006).

Ten of the 14 participants in the experimental group completed the Raven’s progressive matrices (RPM) that measures analytical reasoning and fluid intelligence (Raven et al. 2003) and which is recommended as a short, nonverbal test of intelligence in autism (Bölte et al., 2009; Dawson et al., 2007). Four participants did not complete the test due to personal time constraints when visiting the laboratory, and their parents did not manage to complete the assignment at home. Of these four, three were attending mainstream secondary school and are expected to have scores in the normal range consistent with school records. For the remaining participants who did not complete the Ravens, school records show Wechsler Intelligence Scale for Children (WISC-III) (Wechsler, 1991) scores with above-average verbal performance and below-average performance scores. For the 10 tested, scores ranged from 18 to 52 with a mean score of 41.5 (SD = 12.37). As a measure of the magnitude of autistic traits, Autism-Spectrum Quotient scores were obtained for 12 of the 14 participants, their parents completing the Adolescent Autism-Spectrum Quotient (AQ; Baron-Cohen et al., 2006). Scores ranged from 23 to 48 with a mean score of 33.67 (SD = 7.59). The typically developing participants did not complete the AQ as norms are available from Baron-Cohen et al. (2006) where 0% of a typically developing sample of adolescent boys scored at or above 30.

Fourteen typically developing male participants were recruited from a mainstream secondary school. They ranged in age from 12 to 15 years, with a mean age of 14.16 years (SD = 0.83 years). Their RPM scores ranged from 34 to 53 with a mean score of 45.00 (SD = 5.38). The experimental and typically developing groups did not differ significantly in age, t = −0.84, df = 19.51, p = 0.40 or in RPM scores, t = −0.84, df = 11.45, p = 0.42. Demographic details for both groups are provided in Table 1. All participants had normal or corrected-to-normal visual acuity. The study was approved by the University College Dublin (UCD) Human Research Ethics Committee and by the Irish Health Services Executive.

Table 1.

Demographic details of the participants.

	Autism spectrum disorders (ASD) group (N = 14, all male)			Typically developing group (N = 14, all male)
	Mean	SD	Range	Mean	SD	Range
Age in years	13.74	1.60	11–17	14.16	0.83	12–15
RPM	41.5	12.37	18–52	45.00	5.38	34–53
AQ	33.67	7.59	23–48

RPM: Raven’s progressive matrices score; AQ: Adolescent Autism Spectrum Quotient.

Stimuli

Digital images of five male and five female unfamiliar faces, in front pose with neutral expression, from a database maintained at UCD were processed in Adobe Photoshop^® to vignette the face (including the inner but excluding the outer hairline), to centre it within a grey background and to ensure that the eyes were aligned horizontally. Duplicates of the 10 images were then ‘Thatcherized’ in Photoshop: three rectangular regions encompassing the eyes and mouth were inverted within the face and then airbrushed to smooth over sharp contours and shadows. Each face was rotated clockwise and saved at seven orientations (0°, 30°, 60°, 90°, 120°, 150°, 180°) in red green blue (RGB) 8-bit colour format. See Figure 1 for an example.

Procedure

The experiment was run on a Dell PC using Presentation^® with the display running at 60 Hz and a spatial resolution of 1024 by 768 pixels. The 140 trials (10 faces, each at seven orientations in both Thatcherized and normal form) were presented in pseudo-random order. On each trial, an image was presented in the centre of the screen and subtended ~26 by 35 degrees of visual angle at ~50 cm. The participant indicated whether the face appeared normal or distorted by pressing one of the two keys on the keyboard, and the key press initiated the next trial. The word ‘distorted’ was also explained as ‘weird’ and ‘strange’ to the adolescent participants. Participants were asked to respond as quickly as possible when confident of their choice. Each participant completed 10 practice trials before the 140 experimental trials.

Results

Error and RT data were analysed in R (R Development Core Team, 2010) using analysis of variance (ANOVA) with a between-subjects factor of Group (ASD/typically developing) and within-subjects factors of Orientation (seven levels) and Condition (Normal/Distorted). Greenhouse–Geisser epsilon (ϵ) corrections are reported when Mauchly’s Test for Sphericity is significant and effect sizes are given by generalized eta squared $η_{G}^{2}$ (Bakeman, 2005). The Chow test (Chow, 1960) was used to explore whether the switch from configural to feature-based processing occurs abruptly as suggested by previous authors (Murray et al., 2000; Stürzel and Spillmann, 2000), with separate analyses performed for the two groups of adolescents.

Errors

Percentage error is plotted in Figure 2. While the adolescents with ASD appear slightly more error-prone than the typically developing adolescents, the groups show very similar profiles. Errors are fairly constant across orientation for normal faces, but for Thatcherized faces, errors increase with orientation and show a marked nonlinearity at ~90° where they rise sharply.

Figure 2.

Error is plotted as a function of angle of rotation from upright for both the normal (blue) and Thatcherized (red) faces for (a) adolescents with ASD and (b) typically developing adolescents. Error bars show ±1 standard error of the mean (SEM). (Colour figures in online version.)

ANOVA showed a significant effect of Condition, F(1,26) = 38.67, p < 0.001, $η_{G}^{2}$ = 0.24, of Orientation, F(6,156) = 48.75, p < 0.001, ϵ = 0.44, $η_{G}^{2}$ = 0.31, and a significant Orientation × Condition interaction, F(6,156) = 27.98, p < 0.001, ϵ = 0.39, $η_{G}^{2}$ = 0.25. The effect of Group did not reach significance at convention levels, F(1,26) = 3.01, p = 0.09. None of the interactions involving Group were significant (with Orientation, p = 0.83, with Condition, p = 0.39, with Orientation × Condition, p = 0.99). Post hoc tests showed that the effect of Orientation was highly significant for Thatcherized faces, F(6,162) = 44.31, p < 0.001, ϵ = 0.36, $η_{G}^{2}$ = 0.47, but not for normal faces, F(6,162) = 1.80, p < 0.001, ϵ = 0.69 and $η_{G}^{2}$ = 0.03.

The obvious break in the error data was further explored using the Chow test with a breakpoint of 90°. The Chow test tests for a structural break in a data set by comparing whether regression coefficients estimated over one subset of the data (here, over orientations of 90° or less) are equal to those estimated over another (here, over orientations greater than 90°), by looking at how much the sum of squared residuals falls when the regression is estimated separately for each subset of data (Chow, 1960). This test was significant for the Thatcherized faces for both the ASD, F(2,94) = 3.25, p = 0.04, and typically developing, F(2,94) = 5.52, p = 0.005, groups, but not for the normal faces for either the ASD, F(2,94) = 0.02, p = 0.98, or typically developing, F(2,94) = 0.14, p = 0.87, group.

RTs

Analyses were carried out for correct trials only; 91.53% (94.59%) of normal and 69.69% (78.16%) of Thatcherized trials for the ASD (and typically developing) group. After removing RTs less than 250 ms, RTs, examined separately by participant and condition, were ranked and obvious outliers (exceeding the last highest by a jump of 2 s or more) were also removed. In total, 1.33% (0.125%) of correct trials for the ASD (typically developing) group was removed. Mean imputation was used to replace four cases of missing data (at 150° and 180°) in the ASD data set (i.e. cases where a participant got all 10 trials incorrect) using the average value for the other participants and to replace two cases of missing data (at 150° and 180°) in the typically developing data set.

Mean RT is plotted in Figure 3 with polynomial regression fits used for illustrative purposes. The normal faces data were best fit by a linear model, while a quadratic model was used for the Thatcherized faces data. As previously reported for the Thatcher illusion (Lewis, 2001), participants are faster to identify Thatcherized than normal faces at upright but not at inverted orientations, the plots crossing between 90° and 120° for the typically developing group and between 90° and 150° for the ASD group.

Figure 3.

RT is plotted as a function of angle of rotation from upright for both the normal (blue) and Thatcherized (red) faces for (a) adolescents with ASD and (b) typically developing adolescents. The solid blue and red lines show polynomial regression fits.

ANOVA showed a significant effect of Orientation, F(6,156) = 30.54, p < 0.001, ϵ = 0.54, $η_{G}^{2}$ = 0.10, and a significant Orientation × Condition interaction, F(6,156) = 12.30, p < 0.001, ϵ = 0.59, $η_{G}^{2}$ = 0.03. The effect of Group was not significant, F(1,26) = 0.85, p = 0.36, and none of the interactions involving Group were significant (all p-values > 0.40). Post hoc tests showed that Orientation was highly significant in both the Thatcherized, F(6,162) = 29.28, p < 0.001, ϵ = 0.55, $η_{G}^{2}$ = 0.31, and the normal, F(6,162) = 6.77, p < 0.001, ϵ = 0.61, $η_{G}^{2}$ = 0.02, condition.

As the RT data show no obvious breakpoints, these were estimated using the ‘strucchange’ package in R (Zeileis et al., 2002). Using breakpoints estimated at 150° for the normal faces, the Chow test was not significant for either the ASD, F(2,94) = 0.12, p = 0.87, or typically developing, F(2,94) = 1.37, p = 0.26, group. For the Thatcherized faces data, and using an estimated breakpoint at 120°, the Chow test was not significant for the ASD group, F(2,94) = 2.30, p = 0.11, but was significant for an estimated breakpoint at 150° for the typically developing group, F(2,94) = 5.34, p < 0.01. The decrease in RT from 150° to 180° shown by the typically developing group with Thatcherized faces is also seen in Lewis (2001).

Discussion

This study shows that adolescents with ASD perform similarly to typically developing adolescents in their perception of distorted faces. First, the presence of a strong inversion effect, as measured by both RT and error rates, replicates the findings of two previous studies on the perception of the Thatcher illusion in children and adolescents with ASD (Riby et al., 2009; Rouse et al., 2004). Secondly, novel to this study is the finding that adolescents with ASD, like the typically developing adolescents, show a marked nonlinearity in their error by orientation profiles such that error is low and independent of orientation for angles ≤90° and then rises sharply for angles >90°. This suggests a relatively abrupt shift from configural processing that operates over a range of orientations at or close to the upright to a more feature- or componential-based strategy at inverted orientations and greatly strengthens the conclusion that configural processing of face is intact in ASD.

We first consider the error data that prove particularly informative. As in previous studies of the Thatcher illusion, including those with clinical groups (Riby et al., 2009; Rouse et al., 2004; Zürcher et al., 2013), participants show a marked increase in error at inverted relative to upright orientations for Thatcherized but not for normal faces. While those with ASD are somewhat more error-prone in our study, the group difference approaching significance at p = 0.09, error for both groups is similarly affected by stimulus type and by orientation. Specifically, neither the Group × Orientation (p = 0.83) nor the Group × Orientation × Condition (p = 0.99) interactions are significant. This evidence for an inversion effect, whereby the perception of distortion is greatly hampered for inverted faces, argues for intact configural processing in ASD. Examination of the error by orientation profiles for the Thatcherized faces shows a clear nonlinearity whereby error is roughly constant out to 90° and then rises sharply with further rotation of the faces from the upright for both groups of adolescents. The Chow test, normally associated with econometric research, provides a simple and elegant way to confirm a structural break in the data. The sudden shift in error that occurs at 90° strengthens the idea that configural processing is disrupted by inversion, and that this disruption occurs when the faces are rotated outside the range of orientations at which they are normally perceived (Murray et al., 2000; Stürzel and Spillmann, 2000). The fact that the adolescents with ASD show the same error by orientation profile as the typically developing adolescents suggests that they too are sensitive to the normal orientation of faces and have developed specialized configural processing mechanisms as an efficient means to represent them.

Turning to RTs, both groups of adolescences performed comparably to the (neurotypical) adult participants in Lewis’ (2001) study. Specifically, they show a gradual increase in RT as the faces are rotated away from the upright and towards the inverted, this increase in RT being steeper for Thatcherized than normal faces. For both groups, the RT by orientation curves for the two conditions cross somewhere between 90° and 120°, previously suggested by Lewis (2001) to indicate a shift from configural to local processing. Unlike the error data, there are no very obvious structural breakpoints in the Thatcherized faces data. Those estimated are at larger angles of rotation (120° and 150°) and reflect a decline in the rate of increase in RT as the stimulus is rotated towards the fully inverted position. This is also evident in Lewis’ (2001) RT data for the Thatcherized faces and may simply reflect the fact that restoring the symmetry of the stimulus about the vertical axis makes the judgement easier and therefore quicker.

In summary, the results of our experiment agree with those of two former studies of the Thatcher illusion in young people with ASD. These show that children (Rouse et al., 2004) and adolescents (Riby et al., 2009) show inversion effects in the perception of the distorted faces as measured by both RT (Rouse et al., 2004) and error rates (Riby et al., 2009; Rouse et al., 2004). Both those studies used a modified version of the Thatcher illusion – introduced by Rouse et al. (2004) for young children – in which Thatcherized and normal faces were positioned side by side and participants indicated which one appeared strange. Our results extend their findings using the more conventional method, whereby participants make a perceptual judgment about a single face on each trial in an explicitly timed task. The presence of a strong inversion effect, as shown here for both groups of adolescents, is indicative of intact configural processing (Maurer et al., 2002; Weigelt et al., 2012). Additionally, testing at multiple orientations between the upright and inverted allows us to examine where the switch in processing occurs. Interestingly, an analysis of the error data suggests a relatively abrupt switch in processing at 90° as previously reported for neurotypical adult samples (Murray et al., 2000; Stürzel and Spillmann, 2000), whereas an examination of RT data suggests a more gradual shift as also seen in Lewis (2001).

There are limitations to our study that should be noted. Participants in our experimental group were, in general, intellectually able (with one participant showing mild and another moderate intellectual impairment), and they varied in their AQ scores that provide a measure of the magnitude of autistic traits. In Riby et al. (2009), 11 of the 20 children tested were classified as mild-to-moderately autistic and 9 as severely autistic, whereas in Rouse et al. (2004), all 11 participants had mild intellectual impairment. The difference in overall error scores between our groups (which approaches significance at p = 0.09) likely reflects the greater spread of intellectual functioning, but, as in these former studies, the inversion effect is not diminished or absent in the ASD group. Although our results are therefore consistent with others, replication with a larger sample size would allow for a more rigorous comparison of participants with different levels of intellectual functioning.

Finally, we note that these findings are not incompatible with results showing that people with autism show superior performance in the perception of local detail in other cognitive tasks such as the block design task, the embedded figures task and in visual search tasks (Jolliffe and Baron-Cohen, 1997; O’Riordan et al., 2001; Shah and Frith, 1993) but suggest that for the special case of face perception, those with ASD process faces in a way that is qualitatively similar to typically developing adolescents as suggested by recent reviews (Weigelt et al., 2012). In particular, the finding that adolescents with ASD show an abrupt and marked increase in error as faces are rotated beyond 90° suggests that configural processing, at least as measured by the Thatcher illusion, is intact and operates over the same range of orientations as in the neurotypical population.

Footnotes

Acknowledgements

We are grateful to the teenagers who participated and to their parents who facilitated their participation.

Funding

This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors.

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