WAVEMIXSR-V2: ENHANCING SUPER-RESOLUTION WITH HIGHER EFFICIENCY
WAVEMIXSR-V2：以更高效率增强超分辨率
ABSTRACT
摘要
Recent advancements in single image super-resolution have been predominantly driven by token mixers and transformer architectures. WaveMixSR utilized the WaveMix architecture, employing a two-dimensional discrete wavelet transform for spatial token mixing, achieving superior performance in super-resolution tasks with remarkable resource efficiency. In this work, we present an enhanced version of the WaveMixSR architecture by (1) replacing the traditional transpose convolution layer with a pixel shuffle operation and (2) implementing a multistage design for higher resolution tasks $(4\times)$ . Our experiments demonstrate that our enhanced model – WaveMixSR-V2 – outperforms other architectures in multiple super-resolution tasks, achieving state-of-the-art for the BSD100 dataset, while also consuming fewer resources, exhibits higher parameter efficiency, lower latency and higher throughput. Our code is available at https://github.com/prana v phoenix/WaveMixSR
单幅图像超分辨率领域的最新进展主要由token mixer和Transformer架构推动。WaveMixSR采用WaveMix架构，通过二维离散小波变换实现空间token混合，在超分辨率任务中表现出卓越性能且资源效率极高。本研究提出WaveMixSR架构的增强版本：(1) 用像素洗牌操作替代传统转置卷积层；(2) 针对更高分辨率任务$(4\times)$实现多阶段设计。实验表明增强版模型WaveMixSR-V2在多项超分辨率任务中超越其他架构，在BSD100数据集上达到最先进水平，同时具有更低资源消耗、更高参数效率、更低延迟和更高吞吐量。代码详见https://github.com/prana v phoenix/WaveMixSR
Keywords Image super-resolution $\cdot$ resource-efficient $\cdot$ architecture $\cdot$ wavelet transform
关键词 图像超分辨率 $\cdot$ 资源高效 $\cdot$ 架构 $\cdot$ 小波变换
Figure 1: Comparison of PSNR and SSIM for $2\times$ SR on BSD100 dataset shows WaveMixSR-V2 surpasses the previous state-of-the-art WaveMixSR and other methods such as HAT and SwinFIR. $4\times$ SR results in Appendix.
图 1: 在BSD100数据集上进行的2倍超分辨率(Super-Resolution)PSNR与SSIM指标对比显示，WaveMixSR-V2超越了先前最先进的WaveMixSR以及HAT、SwinFIR等方法。4倍超分辨率结果见附录。
1 Introduction
1 引言
Single-image super-resolution (SISR) is a key task in image reconstruction, aiming to transform low-resolution (LR) images into high-resolution (HR) by predicting and restoring missing details. This process requires capturing both local information and global context. Recent advancements in super-resolution, particularly with attention-based transformers like SwinFIR [1] and hybrid attention transformer [2], have surpassed traditional CNN approaches due to their ability to capture long-range dependencies. However, transformers face challenges with quadratic complexity in self-attention, leading to high resource demands and requiring large datasets. To overcome this, token-mixer models such as WaveMixSR [3], which uses a two-dimensional discrete wavelet transform, have shown potential for improved efficiency and even superior performance. Building on the strengths of WaveMixSR, we propose enhancements to the model by rethinking its upsampling strategy inside the WaveMix blocks and changing the single stage design. Details of architecture, more results, including those on $4\times\mathrm{SR}$ , and ablation studies are provided in the Appendix.
单图像超分辨率 (SISR) 是图像重建中的关键任务，旨在通过预测和恢复缺失细节将低分辨率 (LR) 图像转换为高分辨率 (HR) 。该过程需要同时捕获局部信息和全局上下文。近年来，超分辨率领域的技术进步，尤其是基于注意力机制的 Transformer 模型（如 SwinFIR [1] 和混合注意力 Transformer [2]），因其能够捕捉长距离依赖关系，已超越传统的 CNN 方法。然而，Transformer 面临自注意力二次复杂度带来的挑战，导致资源需求高且依赖大规模数据集。为解决这一问题，诸如 WaveMixSR [3] 这类采用二维离散小波变换的 Token 混合器模型，已展现出提升效率甚至实现更优性能的潜力。基于 WaveMixSR 的优势，我们通过重新思考其 WaveMix 块内的上采样策略并调整单阶段设计，提出了模型改进方案。架构细节、更多结果（包括 $4\times\mathrm{SR}$ 的实验）以及消融研究详见附录。
2 Architectural Improvements
2 架构改进
2.1 Multi-stage Design
2.1 多阶段设计
We have made significant improvements to the WaveMixSR model, focusing on two key aspects. First, we addressed how the model handles SR tasks higher than $2\times$ . In the original WaveMixSR [3], all SR tasks were performed by directly resizing the LR image to HR using a single upsampling layer. This layer relied on non-parametric upsampling techniques, such as bilinear or bicubic interpolation, which limited the model’s ability to fine-tune and optimize the SR process across different scales. Our approach involved transitioning from this single-stage design to a more robust multi-stage design. In our new architecture, we introduced a series of resolution-doubling $2\times$ SR blocks, which progressively doubles the resolution step by step. This multi-stage approach allows for better SR performance at higher scales while reducing resource consumption.
我们对WaveMixSR模型进行了重大改进，重点聚焦于两个关键方面。首先，针对模型处理超过$2\times$的超分辨率(SR)任务的方式进行了优化。原始WaveMixSR [3]中，所有SR任务都是通过单个上采样层直接将低分辨率(LR)图像缩放到高分辨率(HR)，该层依赖双线性或双三次插值等非参数化上采样技术，限制了模型在不同尺度下微调和优化SR过程的能力。我们的解决方案是将这种单阶段设计转变为更鲁棒的多阶段设计。在新架构中，我们引入了一系列分辨率翻倍的$2\times$ SR模块，逐步实现分辨率倍增。这种多阶段方法能在更高尺度下获得更好的SR性能，同时降低资源消耗。
Figure 2: Architecture of WaveMixSR-V2 showing $4\times$ SR with two $2\times$ SR blocks in series. Details in Appendix.
图 2: WaveMixSR-V2架构示意图，展示通过两个串联的 $2\times$ 超分模块实现 $4\times$ 超分辨率。详见附录。
For instance, in an $4\times$ super-resolution task, instead of directly upsampling the LR image to HR using a single interpolation layer, the model now proceeds through a series of two $2\times$ SR blocks as shown in Fig. 2 By increment ally increasing the resolution (doubling in each stage), the model is better able to refine the details at each step, leading to superior super-resolution performance compared to the single upsampling operation used in the original WaveMixSR.
例如，在4倍超分辨率任务中，模型不再通过单一插值层直接将低分辨率(LR)图像上采样至高分辨率(HR)，而是如图2所示依次通过两个2倍超分辨率块进行处理。通过分阶段逐步提升分辨率(每阶段翻倍)，模型能更好地在每一步骤中优化细节，从而获得比原始WaveMixSR采用的单次上采样操作更优异的超分辨率性能。
2.2 Pixel Shuffle
2.2 像素洗牌 (Pixel Shuffle)
We introduce a key modification to the WaveMixSR model by replacing the transposed convolution operation in the WaveMix blocks with a Pixel Shuffle [4] operation followed by a convolution layer (WaveMixSR-V2 block) as shown in Fig. 5. While the original WaveMixSR used transposed convolutions, which involved numerous parameters and high computational cost, Pixel Shuffle upsamples the image more efficiently by rearranging pixels from feature maps. This significantly reduces the number of parameters, enhancing the model’s efficiency. The subsequent convolution layer after Pixel Shuffle allows the model to continue learning and refining features effectively. Moreover, Pixel Shuffle avoids the checkerboard artifacts commonly introduced by transposed convolutions, producing smoother and more natural-looking images while maintaining high-quality super-resolution outputs.
我们对WaveMixSR模型进行了一项关键改进：将WaveMix块中的转置卷积操作替换为Pixel Shuffle [4]操作后接卷积层(WaveMixSR-V2块)，如图5所示。原始WaveMixSR使用的转置卷积涉及大量参数且计算成本高，而Pixel Shuffle通过重排特征图像素实现更高效的上采样。这显著减少了参数量，提升了模型效率。Pixel Shuffle后接的卷积层使模型能持续有效地学习和优化特征。此外，Pixel Shuffle避免了转置卷积常见的棋盘伪影，在保持高质量超分辨率输出的同时，能生成更平滑自然的图像。
Incorporating these improvements in the architecture has enabled WaveMixSR-V2 to achieve new state-of-the-art (SOTA) performance on the BSD100 dataset [5]. Notably, it accomplishes this with less than half the number of parameters, lesser computations and lower latency compared to WaveMixSR (previous SOTA).
将这些改进融入架构后，WaveMixSR-V2在BSD100数据集[5]上实现了新的最先进(SOTA)性能。值得注意的是，与WaveMixSR(前SOTA)相比，它用不到一半的参数数量、更少的计算量和更低的延迟实现了这一目标。
References
参考文献
Figure 3: Simplified block diagram of WaveMix block in WaveMixSR (on the left) and WaveMixSR-V2 block (on the right). Details in Appendix.
Table 1: Model complexity comparison of WaveMixSR-V2 with other state-of-the-art methods such as WaveMixSR, SwinIR and HAT on $4\times\mathrm{SR}$ of $64\times64$ input patch.
图 3: WaveMixSR 中的 WaveMix 模块简化框图(左)和 WaveMixSR-V2 模块(右)。详情见附录。
| 模型 | 参数量 | 乘加运算量 |
|---|---|---|
| SwinIR [6] | 11.8M | 49.6G |
| HAT [2] | 20.8M | 103.7G |
| WaveMixSR[3] | 1.7M | 25.8G |
| WaveMixSR-V2 | 0.7M | 25.6G |
表 1: WaveMixSR-V2 与其他先进方法(如 WaveMixSR、SwinIR 和 HAT)在 $64\times64$ 输入块 $4\times\mathrm{SR}$ 任务上的模型复杂度对比。
A Architecture
架构
A.1 WaveMixSR-V2 Block
A.1 WaveMixSR-V2 模块
The core part of our super-resolution (SR) architecture are the WaveMixSR-V2 blocks shown in Fig. 4(c). We created these by modifying the WaveMix [7] blocks used in WaveMixSR model [3]. We replace the transposed convolution used in WaveMix block with a Pixel Shuffle [4] operation followed by a convolutional layer.
我们超分辨率 (SR) 架构的核心部分是图 4(c) 所示的 WaveMixSR-V2 模块。这些模块是通过修改 WaveMixSR 模型 [3] 中使用的 WaveMix [7] 模块而创建的。我们将 WaveMix 模块中使用的转置卷积替换为 Pixel Shuffle [4] 操作，后接一个卷积层。
Denoting input and output tensors of the WaveMixSR-V2 block by ${\bf{X}}{i n}$ and $\mathbf{X}{O u t}$ , respectively; the four wavelet filters along with their down sampling operations at each level by $w_{a a},w_{a d},w_{d a},w_{d d}$ ( $\mathit{\check{a}}$ for approximation, $d$ for detail); convolution, multi-layer perceptron (MLP), Pixel Shuffle, and batch normalization operations by $c,m,p$ , and $b$ , respectively; and their respective trainable parameter sets by $\xi,\theta,\phi$ , and $\gamma$ , respectively; concatenation along the channel dimension by $\bigoplus$ , and point-wise addition by $^+$ , the operations inside a WaveMixSR-V2 block can be expressed using the following equations:
将 WaveMixSR-V2 块的输入和输出张量分别表示为 ${\bf{X}}{i n}$ 和 $\mathbf{X}{O u t}$；四个小波滤波器及其每层的下采样操作为 $w_{a a},w_{a d},w_{d a},w_{d d}$（$\mathit{\check{a}}$ 表示近似，$d$ 表示细节）；卷积、多层感知机 (MLP)、Pixel Shuffle 和批量归一化操作分别表示为 $c,m,p$ 和 $b$；它们各自的可训练参数集分别为 $\xi,\theta,\phi$ 和 $\gamma$；沿通道维度的拼接操作为 $\bigoplus$，逐点相加操作为 $^+$，则 WaveMixSR-V2 块内的操作可用以下公式表示：
$$
\mathbf{x}{0}=c(\mathbf{x}{i n},\boldsymbol{\xi});~\mathbf{x}{i n}\in\mathbb{R}^{H\times W\times C},\mathbf{x}_{0}\in\mathbb{R}^{H\times W\times C/4}
$$
$$
\mathbf{x}{0}=c(\mathbf{x}{i n},\boldsymbol{\xi});~\mathbf{x}{i n}\in\mathbb{R}^{H\times W\times C},\mathbf{x}_{0}\in\mathbb{R}^{H\times W\times C/4}
$$
$$
\mathbf{x}=[w_{a a}(\mathbf{x}{0})\oplus w_{a d}(\mathbf{x}{0})\oplus w_{d a}(\mathbf{x}{0})\oplus w_{d d}(\mathbf{x}_{0})];~\mathbf{x}\in\mathbb{R}^{H/2\times W/2\times4C/4}
$$
$$
\mathbf{x}=[w_{a a}(\mathbf{x}{0})\oplus w_{a d}(\mathbf{x}{0})\oplus w_{d a}(\mathbf{x}{0})\oplus w_{d d}(\mathbf{x}_{0})];~\mathbf{x}\in\mathbb{R}^{H/2\times W/2\times4C/4}
$$
$$
\tilde{\mathbf{x}}=b(c(p(m(\mathbf{x},\theta),\phi),\xi),\gamma);~\tilde{\mathbf{x}}\in\mathbb{R}^{H\times W\times C}
$$
$$
\tilde{\mathbf{x}}=b(c(p(m(\mathbf{x},\theta),\phi),\xi),\gamma);~\tilde{\mathbf{x}}\in\mathbb{R}^{H\times W\times C}
$$
$$
\mathbf{x}{o u t}=\tilde{\mathbf{x}}{1}+\mathbf{x}{i n};\qquad\mathbf{x}_{o u t}\in\mathbb{R}^{H\times W\times C}
$$
$$
\mathbf{x}{o u t}=\tilde{\mathbf{x}}{1}+\mathbf{x}{i n};\qquad\mathbf{x}_{o u t}\in\mathbb{R}^{H\times W\times C}
$$
Figure 4: Architecture of WaveMixSR-V2. (a) The application of WaveMixSR-V2 for $4\times$ SR is shown featuring two $2\times$ SR blocks stacked in series. For higher SR tasks, more $2\times$ SR blocks will be added. (b) The details of the $2\times\mathrm{SR}$ block and (c) shows the WaveMixSR-V2 block that replaces the transposed convolution with a Pixel Shuffle operation followed by a convolution.
图 4: WaveMixSR-V2架构。(a) 展示了WaveMixSR-V2在$4\times$超分辨率(SR)任务中的应用，采用两个串联的$2\times$ SR模块堆叠而成。对于更高倍率的SR任务，将添加更多$2\times$ SR模块。(b) $2\times\mathrm{SR}$模块的详细结构，(c) 展示了用Pixel Shuffle操作替代转置卷积、后接常规卷积的WaveMixSR-V2模块。
The WaveMixSR-V2 block extracts learnable and space-invariant features using a convolutional layer, followed by spatial token-mixing and down sampling for scale-invariant feature extraction using 2 dimenional-discrete wavelet transform (2D-DWT) [13], followed by channel-mixing using a learnable MLP ( $1\times1$ conv) layer, followed by restoring spatial resolution of the feature map using Pixel Shuffle operation. The use of trainable convolutions before the wavelet transform allows the extraction of only those feature maps that are suitable for the chosen wavelet basis functions. The convolutional layer $c$ decreases the embedding dimension $C$ by a factor of four so that the concatenated output $\mathbf{X}$ after 2D-DWT has the same number of channels as the input ${\bf{X}}_{i n}$ (Eq.1 and Eq.2). That is since 2D-DWT is a lossless transform, it expands the number of channels by the same factor (using concatenation) by which it reduces the spatial resolution by computing an approximation sub-band (low-resolution approximation) and three detail sub-bands (spatial derivatives) [14] for each input channel (Eq.2). The use of this image-appropriate and lossless down sampling using 2D-DWT allows WaveMixSR-V2 to use fewer layers and parameters.
WaveMixSR-V2模块通过卷积层提取可学习且空间不变的特征，随后进行空间token混合，并利用二维离散小波变换(2D-DWT) [13]进行尺度不变特征的下采样，接着通过可学习的MLP( $1\times1$ 卷积)层进行通道混合，最后使用Pixel Shuffle操作恢复特征图的空间分辨率。在小波变换前使用可训练卷积层，能够仅提取适合所选小波基函数的特征图。卷积层 $c$ 将嵌入维度 $C$ 缩减为四分之一，使得2D-DWT后的拼接输出 $\mathbf{X}$ 与输入 ${\bf{X}}_{i n}$ 保持相同通道数(式1与式2)。由于2D-DWT是无损变换，它通过计算每个输入通道的近似子带(低分辨率近似)和三个细节子带(空间导数) [14] (式2)，在降低空间分辨率的同时以相同倍数(通过拼接)扩展通道数。这种基于图像特性且无损的2D-DWT下采样方式，使得WaveMixSR-V2能够使用更少的层数和参数。
The output $\hat{\bf x}$ is then passed to an MLP layer $m$ , which has two $1\times1$ convolutional layers with an inverse bottleneck design (multiplication factor $>1$ ) separated by a GELU non-linearity. After this, the feature map resolution is doubled using Pixel Shuffle operation $p$ . Since Pixel Shuffle reduces the channel dimension by 4, we use another convolution layer $c$ to increase the channel dimension back to $C$ . This is followed by batch normalization $b$ (Eq.3). A residual connection is used to ease the flow of the gradient [15] (Eq.4). The WaveMixSR-V2 block ensures that input and output resolution are the same.
输出 $\hat{\bf x}$ 随后被传递到一个 MLP 层 $m$，该层采用逆瓶颈设计（乘数因子 $>1$），包含两个 $1\times1$ 卷积层，中间通过 GELU 非线性激活函数分隔。此后，使用 Pixel Shuffle 操作 $p$ 将特征图分辨率提升一倍。由于 Pixel Shuffle 会将通道维度减少 4 倍，我们通过另一个卷积层 $c$ 将通道维度恢复至 $C$，随后进行批量归一化 $b$（式3）。采用残差连接以优化梯度流动 [15]（式4）。WaveMixSR-V2 模块确保输入与输出分辨率保持一致。
Among the different types of mother wavelets available, we used the Haar wavelet (a special case of the Daubechies wavelet [14], also known as Db1), which is frequently used due to its simplicity and faster computation. Haar wavelet is both orthogonal and symmetric in nature and has been extensively used to extract basic structural information from images [16]. For even-sized images, it reduces the dimensions exactly by a factor of 2, which simplifies the designing of the subsequent layers.
在可选的小波基函数中，我们采用了Haar小波（Daubechies小波[14]的特例，亦称Db1）。因其计算简单高效而广受青睐，Haar小波兼具正交性与对称性，已被广泛应用于图像基础结构信息提取[16]。对于偶数尺寸图像，它能将维度精确缩减为原尺寸的1/2，从而简化后续网络层的设计。
Figure 5: Visual results of $2\times$ SR on BSD100 dataset. Each column from the left shows a patch from the HR image (shown as a small image near the corner), the same patch extracted from the LR image, and a patch taken from the model output respectively. The filename of the image is given below the HR image and the PSNR/SSIM of the model output is reported at below the model output. The values displayed are computed for the whole image and not just the patch.
图 5: BSD100 数据集上 $2\times$ 超分辨率 (SR) 的视觉结果。从左至右每列分别显示：HR (高分辨率) 图像中的局部区块 (角落以小图展示)、从 LR (低分辨率) 图像提取的相同区块、模型输出对应的区块。HR 图像下方标注文件名，模型输出下方显示其 PSNR/SSIM 指标。所示数值为整幅图像 (而非局部区块) 的计算结果。
Table 2: Quantitative comparison with previous state-of-the-art methods on the BSD100 dataset shows that WaveMixSRV2 performs better using less training data ( $^*$ indicates models that were pre-trained on ImageNet).
表 2: 在BSD100数据集上与先前最先进方法的定量比较表明，WaveMixSRV2使用更少的训练数据表现更好（$^*$表示在ImageNet上预训练的模型）。
| 模型 | 训练数据集 | 2× SR PSNR | 2× SR SSIM | 4× SR PSNR | 4× SR SSIM |
|---|---|---|---|---|---|
| EDSR [8] | DIV2K | 32.32 | 0.9013 | 27.71 | 0.7420 |
| RCAN [9] | DIV2K | 32.41 | 0.9027 | 27.77 | 0.7436 |
| SAN [10] | DIV2K | 32.42 | 0.9028 | 27.78 | 0.7436 |
| IGNN [10] | DIV2K | 32.41 | 0.9025 | 27.77 | 0.7434 |
| HAN [11] | DIV2K | 32.41 | 0.9027 | 27.80 | 0.7442 |
| NLSN [10] | DIV2K | 32.43 | 0.9027 | 27.78 | 0.7444 |
| RCN-it [10] | DF2K | 32.48 | 0.9034 | 27.87 | 0.7459 |
| SwinIR [6] | DF2K | 32.53 | 0.9041 | 27.92 | 0.7489 |
| EDT [12] | DF2K | 32.52 | 0.9041 | 27.91 | 0.7483 |
| HAT [10] | DF2K | 32.62 | 0.9053 | 28.00 | 0.7517 |
| SwinFIR* [1] | DF2K | 32.64 | 0.9054 | 28.03 | 0.7520 |
| HAT-L* [10] | DF2K | 32.74 | 0.9066 | 28.09 | 0.7551 |
| WaveMixSR [3] | DIV2K | 33.08 | 0.9322 | 27.65 | 0.7605 |
| WaveMixSR-V2 | DIV2K | 33.12 | 0.9326 | 27.87 | 0.7640 |
Table 3: Comparison of latency and throughput of WaveMixSR-V2 and WaveMixSR shows that WaveMixSR-V2 is significantly faster than WaveMixSR
| 模型 | 训练延迟 ← (毫秒) | 训练吞吐量 (帧/秒) | 推理延迟 ↓ (毫秒) | 推理吞吐量 ↑ (帧/秒) |
|---|---|---|---|---|
| WaveMixSR | 22.8 | 43.8 | 18.6 | 53.7 |
| WaveMixSR-V2 | 19.6 | 50.8 | 12.1 | 82.6 |
表 3: WaveMixSR-V2与WaveMixSR的延迟和吞吐量对比表明，WaveMixSR-V2显著快于WaveMixSR
A.2 $2\times$ SR Block
A.2 $2\times$ SR 块
As shown in Fig. 4(b), the $2\times\mathrm{SR}$ block has two paths – one for handling the Y channel and another for the CbCr channels of the input image. The Y channel is used for the path with learning using WaveMixSR-V2 blocks because the Y channel contains most of the image details and is less affected by color changes. It first upsamples the image to HR size using a parameter-free upsampling block using bilinear or bicubic interpolation. The output of upsampling block, is sent to a convolutional layer to increase the number of feature maps before sending it to the WaveMixSR-V2 blocks. We connected $L$ WaveMixSR-V2 blocks in series to create high-resolution feature maps. The output from the final WaveMixSR-V2 blocks is then passed through a convolutional layer which reduces the channel dimension and returns a single channel output.
如图4(b)所示，$2\times\mathrm{SR}$模块包含两条路径——一条处理输入图像的Y通道，另一条处理CbCr通道。Y通道路径采用WaveMixSR-V2块进行学习，因为Y通道包含图像大部分细节且受色彩变化影响较小。该路径首先通过双线性/双三次插值的无参数上采样模块将图像上采样至高分辨率(HR)尺寸，随后通过卷积层增加特征图数量，再输入至WaveMixSR-V2块。我们将$L$个WaveMixSR-V2块串联以生成高分辨率特征图，最终通过卷积层降维输出单通道结果。
Table 4: Quantitative results of WaveMixSR-V2 on other benchmark SR datasets
| 尺度 | 2x | 4x |
|---|---|---|
| PSNR | SSIM | |
| Set5 | 35.85 | 0.9522 |
| Set14 | 31.20 | 0.9000 |
| Urban100 | 29.20 | 0.9076 |
表 4: WaveMixSR-V2 在其他基准超分辨率数据集上的定量结果
Table 5: Quantitative comparison of WaveMixSR-V2 on benchmark datasets when using different combination of losses for various input resolutions.
表 5: WaveMixSR-V2 在不同输入分辨率下使用不同损失组合时在基准数据集上的定量比较。
| 输入分辨率 | 像素损失 入o | 内容损失 入1 | 对抗损失 入2 | 是否添加噪声 | BSD100 PSNR | BSD100 SSIM | Set5 PSNR | Set5 SSIM | Set14 PSNR | Set14 SSIM | Urban100 PSNR | Urban100 SSIM |
|------------|--------------|--------------|--------------|--------------|-------------|-------------|-----------|-----------|------------|-----
