RuntimeError: expected backend CUDA and dtype Float but got backend CPU and dtype Float

copyrightly: <p>I want to use a custom filter in CNN. The filter has size 5*5 and each entry is a function of three variables: theta, Lambda, psi. There are two convolutional layers followed by two fully connected layers. I tested my filter on MNIST dataset. But when I run it on GPU, I encounter the error: <strong>RuntimeError: expected backend CUDA and dtype Float but got backend CPU and dtype Float</strong>. I guess it might be due to how I generate the filter box, but I cannot find where I made mistake exactly. Basically I modified this <a href="https://github.com/pytorch/examples/blob/master/mnist/main.py" rel="nofollow noopener">example code</a>, I only modified the network structure with my custom filter. Training and test remained unchanged. I attach my code here. Thank you!</p>
<pre><code class="lang-auto">from __future__ import print_function
import argparse
import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim
from torch.autograd import Variable
from torchvision import datasets, transforms


class Net(nn.Module):
    def __init__(self, kernel_size, in_channels, channel1, channel2):
        super(Net, self).__init__()
        self.theta1, self.Lambda1, self.psi1, self.bias1 = self.generate_parameters(channel1, in_channels)
        self.filter1 = self.whole_filter(in_channels, channel1, kernel_size, self.theta1, self.Lambda1, self.psi1).cuda()

        self.theta2, self.Lambda2, self.psi2, self.bias2 = self.generate_parameters(channel2, channel1)
        self.filter2 = self.whole_filter(channel1, channel2, kernel_size, self.theta2, self.Lambda2, self.psi2).cuda()
        self.fc1 = nn.Linear(4*4*50, 500)
        self.fc2 = nn.Linear(500, 10)


    def forward(self, x):
        x = F.conv2d(x, self.filter1, bias=self.bias1)
        x = F.max_pool2d(x, 2, 2)
        x = F.conv2d(x, self.filter2, bias=self.bias2)
        x = F.max_pool2d(x, 2, 2)
        x = x.view(-1, 4*4*50)
        x = F.relu(self.fc1(x))
        x = self.fc2(x)
        return F.log_softmax(x, dim=1)


    def generate_parameters(self, dim_out, dim_in):
        theta = nn.Parameter(torch.randn(dim_out, dim_in))
        Lambda = nn.Parameter(torch.randn(dim_out, dim_in))
        psi = nn.Parameter(torch.randn(dim_out, dim_in))
        bias = nn.Parameter(torch.randn(dim_out))
        return theta, Lambda, psi, bias


    def whole_filter(self, in_channels, out_channels, kernel_size, theta_column, Lambda_column, psi_column):
        result = torch.zeros(out_channels, in_channels, kernel_size, kernel_size) # \text{out\_channels} , \frac{\text{in\_channels}}{\text{groups}} , kH , kW
        for i in range(out_channels):
            result[i] = self.one_filter(in_channels, kernel_size, theta_column[i], Lambda_column[i], psi_column[i])
        return result


    def one_filter(self, in_channels, kernel_size, theta, Lambda, psi):
        result = torch.zeros(in_channels, kernel_size, kernel_size)
        for i in range(in_channels):
            result[i] = self.filter_fn(theta[i], Lambda[i], psi[i], kernel_size)
        return result


    def filter_fn(self, theta, Lambda, psi, kernel_size):
        # Bounding box
        half_size = (kernel_size - 1) // 2
        ymin, xmin = -half_size, -half_size
        ymax, xmax = half_size, half_size
        (y, x) = np.meshgrid(np.arange(ymin, ymax + 1), np.arange(xmin, xmax + 1))
        y = torch.FloatTensor(y)
        x = torch.FloatTensor(x)

        # Rotation
        x_theta = x * torch.cos(theta) + y * torch.sin(theta)
        y_theta = -x * torch.sin(theta) + y * torch.cos(theta)

        box = torch.cos(y_theta) * torch.sin(2 * np.pi / Lambda * x_theta + psi)
        return box



def train(args, model, device, train_loader, optimizer, epoch):
    model.train()
    for batch_idx, (data, target) in enumerate(train_loader):
        data, target = data.to(device), target.to(device)
        optimizer.zero_grad()
        output = model(data)
        loss = F.nll_loss(output, target)
        loss.backward(retain_graph=True)
        optimizer.step()
        if batch_idx % args.log_interval == 0:
            print('Train Epoch: {} [{}/{} ({:.0f}%)]\tLoss: {:.6f}'.format(
                epoch, batch_idx * len(data), len(train_loader.dataset),
                100. * batch_idx / len(train_loader), loss.item()))

def test(args, model, device, test_loader):
    model.eval()
    test_loss = 0
    correct = 0
    with torch.no_grad():
        for data, target in test_loader:
            data, target = data.to(device), target.to(device)
            output = model(data)
            test_loss += F.nll_loss(output, target, reduction='sum').item() # sum up batch loss
            pred = output.argmax(dim=1, keepdim=True) # get the index of the max log-probability
            correct += pred.eq(target.view_as(pred)).sum().item()

    test_loss /= len(test_loader.dataset)

    print('\nTest set: Average loss: {:.4f}, Accuracy: {}/{} ({:.0f}%)\n'.format(
        test_loss, correct, len(test_loader.dataset),
        100. * correct / len(test_loader.dataset)))

def main():
    # Training settings
    parser = argparse.ArgumentParser(description='PyTorch MNIST Example')
    parser.add_argument('--batch-size', type=int, default=64, metavar='N',
                        help='input batch size for training (default: 64)')
    parser.add_argument('--test-batch-size', type=int, default=1000, metavar='N',
                        help='input batch size for testing (default: 1000)')
    parser.add_argument('--epochs', type=int, default=10, metavar='N',
                        help='number of epochs to train (default: 10)')
    parser.add_argument('--lr', type=float, default=0.01, metavar='LR',
                        help='learning rate (default: 0.01)')
    parser.add_argument('--momentum', type=float, default=0.5, metavar='M',
                        help='SGD momentum (default: 0.5)')
    parser.add_argument('--no-cuda', action='store_true', default=False,
                        help='disables CUDA training')
    parser.add_argument('--seed', type=int, default=1, metavar='S',
                        help='random seed (default: 1)')
    parser.add_argument('--log-interval', type=int, default=10, metavar='N',
                        help='how many batches to wait before logging training status')
    parser.add_argument('--save-model', action='store_true', default=False,
                        help='For Saving the current Model')
    args = parser.parse_args()
    use_cuda = not args.no_cuda and torch.cuda.is_available()

    torch.manual_seed(args.seed)

    device = torch.device("cuda" if use_cuda else "cpu")

    kwargs = {'num_workers': 1, 'pin_memory': True} if use_cuda else {}
    train_loader = torch.utils.data.DataLoader(
        datasets.MNIST('../data', train=True, download=True,
                       transform=transforms.Compose([
                           transforms.ToTensor(),
                           transforms.Normalize((0.1307,), (0.3081,))
                       ])),
        batch_size=args.batch_size, shuffle=True, **kwargs)
    test_loader = torch.utils.data.DataLoader(
        datasets.MNIST('../data', train=False, transform=transforms.Compose([
                           transforms.ToTensor(),
                           transforms.Normalize((0.1307,), (0.3081,))
                       ])),
        batch_size=args.test_batch_size, shuffle=True, **kwargs)


    model = Net(5, 1, 20, 50).to(device)
    optimizer = optim.SGD(model.parameters(), lr=args.lr, momentum=args.momentum)

    for param in model.parameters():
        print(type(param.data), param.size())

    for epoch in range(1, args.epochs + 1):
        train(args, model, device, train_loader, optimizer, epoch)
        test(args, model, device, test_loader)

    if (args.save_model):
        torch.save(model.state_dict(),"mnist_cnn.pt")

if __name__ == '__main__':
    main()

</code></pre>

ptrblck: <p>Try to use <code>nn.Parameter</code> for your return values in <code>whole_filter</code> and <code>one_filter</code>, as this will properly register these filters as internal parameters, and will thus push them also to the GPU in the <code>model.to(device)</code> call.</p>

copyrightly: <p>Hi Ptrblck, I added <code>nn.Parameter</code> and it works! Thank you very much!! A further question: when I deleted <code>.cuda()</code> in <code>self.filter1</code> and <code>self.filter2</code>, the parameters have size:</p>
<pre><code class="lang-auto">&lt;class 'torch.Tensor'&gt; torch.Size([20, 1])
&lt;class 'torch.Tensor'&gt; torch.Size([20, 1])
&lt;class 'torch.Tensor'&gt; torch.Size([20, 1])
&lt;class 'torch.Tensor'&gt; torch.Size([20])
&lt;class 'torch.Tensor'&gt; torch.Size([20, 1, 5, 5])
&lt;class 'torch.Tensor'&gt; torch.Size([50, 20])
&lt;class 'torch.Tensor'&gt; torch.Size([50, 20])
&lt;class 'torch.Tensor'&gt; torch.Size([50, 20])
&lt;class 'torch.Tensor'&gt; torch.Size([50])
&lt;class 'torch.Tensor'&gt; torch.Size([50, 20, 5, 5])
&lt;class 'torch.Tensor'&gt; torch.Size([500, 800])
&lt;class 'torch.Tensor'&gt; torch.Size([500])
&lt;class 'torch.Tensor'&gt; torch.Size([10, 500])
&lt;class 'torch.Tensor'&gt; torch.Size([10])
</code></pre>
<p>It’s wrong, I should not have the parameters with size ([20, 1, 5, 5]) and ([50, 20, 5, 5]), since I am not using the conventional convolution kernel here. Moreover, the loss is <code>nan</code> during training. But when I keep <code>.cuda()</code> there, it’s correct and training is ok:</p>
<pre><code class="lang-auto">&lt;class 'torch.Tensor'&gt; torch.Size([20, 1])
&lt;class 'torch.Tensor'&gt; torch.Size([20, 1])
&lt;class 'torch.Tensor'&gt; torch.Size([20, 1])
&lt;class 'torch.Tensor'&gt; torch.Size([20])
&lt;class 'torch.Tensor'&gt; torch.Size([50, 20])
&lt;class 'torch.Tensor'&gt; torch.Size([50, 20])
&lt;class 'torch.Tensor'&gt; torch.Size([50, 20])
&lt;class 'torch.Tensor'&gt; torch.Size([50])
&lt;class 'torch.Tensor'&gt; torch.Size([500, 800])
&lt;class 'torch.Tensor'&gt; torch.Size([500])
&lt;class 'torch.Tensor'&gt; torch.Size([10, 500])
&lt;class 'torch.Tensor'&gt; torch.Size([10])
</code></pre>
<p>So I am curious why I cannot delete <code>.cuda()</code>, since you mentioned that <code>nn.Parameter</code> already put the filters on GPU. Thanks a lot!</p>

ptrblck: <p>The <code>.cuda()</code> call shouldn’t change the shape of a tensor.<br>
Could you point me to the line of code or tensor name, which has the shape <code>[20, 1, 5, 5]</code> now?</p>

copyrightly: <p>That happens when I dropped <code>.cuda()</code> at line 16 and 19:</p>
<pre><code class="lang-auto">self.filter1 = self.whole_filter(in_channels, channel1, kernel_size, self.theta1, self.Lambda1, self.psi1).cuda()
self.filter2 = self.whole_filter(channel1, channel2, kernel_size, self.theta2, self.Lambda2, self.psi2).cuda()
</code></pre>
<p>My guess is that after I dropped <code>.cuda()</code>, when I call <code>x = F.conv2d(x, self.filter1, bias=self.bias1)</code> on line 25, <code>self.filter1</code> is not on GPU, so pytorch generate a filter of the corresponding size and do the convolution.</p>

ptrblck: <aside class="quote no-group" data-username="copyrightly" data-post="5" data-topic="52617">
<div class="title">
<div class="quote-controls"></div>
<img loading="lazy" alt="" width="24" height="24" src="https://discuss.pytorch.org/letter_avatar_proxy/v4/letter/c/a8b319/48.png" class="avatar"> copyrightly:</div>
<blockquote>
<p>so pytorch generate a filter of the corresponding size and do the convolution.</p>
</blockquote>
</aside>
<p>That shouldn’t be the case, as luckily PyTorch raises a loud <code>RuntimeError</code>, if that’s the case:</p>
<pre data-code-wrap="python"><code class="lang-python">x = torch.randn(1, 1, 4, 4, device='cuda')
filt = torch.randn(6, 1, 3, 3, device='cuda')
output = F.conv2d(x, filt)  # works

filt = filt.cpu()
output = F.conv2d(x, filt)
&gt; RuntimeError: Input type (torch.cuda.FloatTensor) and weight type (torch.FloatTensor) should be the same
</code></pre>

copyrightly: <p>Thank you for you reply. I found out that when I dropped <code>.cuda()</code>, <code>self.filter1</code> and <code>self.filter2</code> appear in <code>model.parameters()</code>, that’s where I got those extra shape. Further in this case, <code>self.bias1</code> and <code>self.bias2</code> have value <code>nan</code>, although <code>self.theta1, self.Lambda1, self.psi1</code> have their value. This makes me quite confused.</p>

ptrblck: <aside class="quote no-group" data-username="copyrightly" data-post="7" data-topic="52617">
<div class="title">
<div class="quote-controls"></div>
<img loading="lazy" alt="" width="24" height="24" src="https://discuss.pytorch.org/letter_avatar_proxy/v4/letter/c/a8b319/48.png" class="avatar"> copyrightly:</div>
<blockquote>
<p>I found out that when I dropped <code>.cuda()</code> , <code>self.filter1</code> and <code>self.filter2</code> appear in <code>model.parameters()</code> , that’s where I got those extra shape.</p>
</blockquote>
</aside>
<p><code>filter1</code> and <code>filter2</code> shouldn’t be returned by <code>model.parameters()</code> regardless of the <code>cuda()</code> call, as they are defined as tensors, not <code>nn.Parameters</code>.<br>
If you want to register them as parameters, warp them in <code>nn.Parameter</code>.</p>
<aside class="quote no-group" data-username="copyrightly" data-post="7" data-topic="52617">
<div class="title">
<div class="quote-controls"></div>
<img loading="lazy" alt="" width="24" height="24" src="https://discuss.pytorch.org/letter_avatar_proxy/v4/letter/c/a8b319/48.png" class="avatar"> copyrightly:</div>
<blockquote>
<p>Further in this case, <code>self.bias1</code> and <code>self.bias2</code> have value <code>nan</code> , although <code>self.theta1, self.Lambda1, self.psi1</code> have their value. This makes me quite confused.</p>
</blockquote>
</aside>
<p>I removed the <code>cuda()</code> call, and changed both filters to be parameters:</p>
<pre data-code-wrap="python"><code class="lang-python">    def whole_filter(self, in_channels, out_channels, kernel_size, theta_column, Lambda_column, psi_column):
        result = torch.zeros(out_channels, in_channels, kernel_size, kernel_size) # \text{out\_channels} , \frac{\text{in\_channels}}{\text{groups}} , kH , kW
        for i in range(out_channels):
            result[i] = self.one_filter(in_channels, kernel_size, theta_column[i], Lambda_column[i], psi_column[i])
        return nn.Parameter(result)
</code></pre>
<p>It seems the model is working for at least one epoch:</p>
<pre data-code-wrap="python"><code class="lang-python">...
Train Epoch: 1 [59520/60000 (99%)]      Loss: 0.054967

Test set: Average loss: 0.1043, Accuracy: 9678/10000 (97%)
</code></pre>

copyrightly: <p>I think I did the same thing as you, however the result is different. Could you run the following code to have a look? (I added <code>nn.Parameter</code> to both <code>one_filter</code> and <code>whole_filter</code> and removed <code>cuda()</code>). Thank you very much for your time!</p>
<pre><code class="lang-auto">from __future__ import print_function
import argparse
import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim
from torch.autograd import Variable
from torchvision import datasets, transforms


class Net(nn.Module):
    def __init__(self, kernel_size, in_channels, channel1, channel2):
        super(Net, self).__init__()
        self.theta1, self.Lambda1, self.psi1, self.bias1 = self.generate_parameters(channel1, in_channels)
        self.filter1 = self.whole_filter(in_channels, channel1, kernel_size, self.theta1, self.Lambda1, self.psi1)

        self.theta2, self.Lambda2, self.psi2, self.bias2 = self.generate_parameters(channel2, channel1)
        self.filter2 = self.whole_filter(channel1, channel2, kernel_size, self.theta2, self.Lambda2, self.psi2)
        self.fc1 = nn.Linear(4*4*50, 500)
        self.fc2 = nn.Linear(500, 10)


    def forward(self, x):
        x = F.conv2d(x, self.filter1, bias=self.bias1)
        x = F.max_pool2d(x, 2, 2)
        x = F.conv2d(x, self.filter2, bias=self.bias2)
        x = F.max_pool2d(x, 2, 2)
        x = x.view(-1, 4*4*50)
        x = F.relu(self.fc1(x))
        x = self.fc2(x)
        return F.log_softmax(x, dim=1)


    def generate_parameters(self, dim_out, dim_in):
        theta = nn.Parameter(torch.randn(dim_out, dim_in))
        Lambda = nn.Parameter(torch.randn(dim_out, dim_in))
        psi = nn.Parameter(torch.randn(dim_out, dim_in))
        bias = nn.Parameter(torch.randn(dim_out))
        return theta, Lambda, psi, bias


    def whole_filter(self, in_channels, out_channels, kernel_size, theta_column, Lambda_column, psi_column):
        result = torch.zeros(out_channels, in_channels, kernel_size, kernel_size) # \text{out\_channels} , \frac{\text{in\_channels}}{\text{groups}} , kH , kW
        for i in range(out_channels):
            result[i] = self.one_filter(in_channels, kernel_size, theta_column[i], Lambda_column[i], psi_column[i])
        return nn.Parameter(result)


    def one_filter(self, in_channels, kernel_size, theta, Lambda, psi):
        result = torch.zeros(in_channels, kernel_size, kernel_size)
        for i in range(in_channels):
            result[i] = self.filter_fn(theta[i], Lambda[i], psi[i], kernel_size)
        return nn.Parameter(result)


    def filter_fn(self, theta, Lambda, psi, kernel_size):
        # Bounding box
        half_size = (kernel_size - 1) // 2
        ymin, xmin = -half_size, -half_size
        ymax, xmax = half_size, half_size
        (y, x) = np.meshgrid(np.arange(ymin, ymax + 1), np.arange(xmin, xmax + 1))
        y = torch.FloatTensor(y)
        x = torch.FloatTensor(x)

        # Rotation
        x_theta = x * torch.cos(theta) + y * torch.sin(theta)
        y_theta = -x * torch.sin(theta) + y * torch.cos(theta)

        box = torch.cos(y_theta) * torch.sin(2 * np.pi / Lambda * x_theta + psi)
        return box



def train(args, model, device, train_loader, optimizer, epoch):
    model.train()
    for batch_idx, (data, target) in enumerate(train_loader):
        data, target = data.to(device), target.to(device)
        optimizer.zero_grad()
        output = model(data)
        loss = F.nll_loss(output, target)
        loss.backward(retain_graph=True)
        optimizer.step()
        if batch_idx % args.log_interval == 0:
            print('Train Epoch: {} [{}/{} ({:.0f}%)]\tLoss: {:.6f}'.format(
                epoch, batch_idx * len(data), len(train_loader.dataset),
                100. * batch_idx / len(train_loader), loss.item()))

def test(args, model, device, test_loader):
    model.eval()
    test_loss = 0
    correct = 0
    with torch.no_grad():
        for data, target in test_loader:
            data, target = data.to(device), target.to(device)
            output = model(data)
            test_loss += F.nll_loss(output, target, reduction='sum').item() # sum up batch loss
            pred = output.argmax(dim=1, keepdim=True) # get the index of the max log-probability
            correct += pred.eq(target.view_as(pred)).sum().item()

    test_loss /= len(test_loader.dataset)

    print('\nTest set: Average loss: {:.4f}, Accuracy: {}/{} ({:.0f}%)\n'.format(
        test_loss, correct, len(test_loader.dataset),
        100. * correct / len(test_loader.dataset)))

def main():
    # Training settings
    parser = argparse.ArgumentParser(description='PyTorch MNIST Example')
    parser.add_argument('--batch-size', type=int, default=64, metavar='N',
                        help='input batch size for training (default: 64)')
    parser.add_argument('--test-batch-size', type=int, default=1000, metavar='N',
                        help='input batch size for testing (default: 1000)')
    parser.add_argument('--epochs', type=int, default=10, metavar='N',
                        help='number of epochs to train (default: 10)')
    parser.add_argument('--lr', type=float, default=0.01, metavar='LR',
                        help='learning rate (default: 0.01)')
    parser.add_argument('--momentum', type=float, default=0.5, metavar='M',
                        help='SGD momentum (default: 0.5)')
    parser.add_argument('--no-cuda', action='store_true', default=False,
                        help='disables CUDA training')
    parser.add_argument('--seed', type=int, default=1, metavar='S',
                        help='random seed (default: 1)')
    parser.add_argument('--log-interval', type=int, default=10, metavar='N',
                        help='how many batches to wait before logging training status')
    parser.add_argument('--save-model', action='store_true', default=False,
                        help='For Saving the current Model')
    args = parser.parse_args()
    use_cuda = not args.no_cuda and torch.cuda.is_available()

    torch.manual_seed(args.seed)

    device = torch.device("cuda" if use_cuda else "cpu")

    kwargs = {'num_workers': 1, 'pin_memory': True} if use_cuda else {}
    train_loader = torch.utils.data.DataLoader(
        datasets.MNIST('../data', train=True, download=True,
                       transform=transforms.Compose([
                           transforms.ToTensor(),
                           transforms.Normalize((0.1307,), (0.3081,))
                       ])),
        batch_size=args.batch_size, shuffle=True, **kwargs)
    test_loader = torch.utils.data.DataLoader(
        datasets.MNIST('../data', train=False, transform=transforms.Compose([
                           transforms.ToTensor(),
                           transforms.Normalize((0.1307,), (0.3081,))
                       ])),
        batch_size=args.test_batch_size, shuffle=True, **kwargs)


    model = Net(5, 1, 20, 50).to(device)
    optimizer = optim.SGD(model.parameters(), lr=args.lr, momentum=args.momentum)

    for param in model.parameters():
        print(type(param.data), param.size())

    for epoch in range(1, args.epochs + 1):
        train(args, model, device, train_loader, optimizer, epoch)
        test(args, model, device, test_loader)
        # for param in model.parameters():
        #     print(param.size(), param.data)
        # print(model.state_dict())
        for name, param in model.state_dict().items():
            print(name, param)

    if (args.save_model):
        torch.save(model.state_dict(),"mnist_cnn.pt")

if __name__ == '__main__':
    main()
</code></pre>

ptrblck: <p>You are right! It seems I was just lucky to have used another seed (in fact running the code line by line a few times) and it seems your parameter initialization might be quite sensitive.<br>
If you set the seed to <code>2809</code> you should get valid results.<br>
However, I would recommend to try to stabilize the training.</p>

copyrightly: <p>Thank you! I set the seed and it works! But the old question still confuses me, why <code>filter1</code> and <code>filter2</code> appear in <code>model.parameters()</code> when I remove <code>cuda()</code>? (I printed out parameters in the code above).</p>

ptrblck: <p>They won’t. If I remove <code>cuda()</code> and the <code>nn.Parameter()</code> wrapping, I’ll get:</p>
<pre><code class="lang-auto">theta1
Lambda1
psi1
bias1
theta2
Lambda2
psi2
bias2
fc1.weight
fc1.bias
fc2.weight
fc2.bias
</code></pre>
<p>Wrapping them in an <code>nn.Parameter</code> will make them appear in <code>model.parameters()</code>.<br>
Could you check, if you were calling <code>nn.Parameter</code> or <code>self.register_parameter</code> somewhere else in the code?</p>

copyrightly: <p>I added <code>nn.Parameter</code> to the returned value of <code>one_filter</code> and <code>whole_filter</code> as you mentioned and I didn’t use <code>self.register_parameter</code>. In my code, <code>filter1</code> and <code>filter2</code> are the returned value of <code>whole_filter</code>, does this make them appear in <code>model.parameters()</code>? But when I added <code>cuda()</code>, they would not appear. You may run my code above to see it. Thank you a lot again!</p>

ptrblck: <p>I might have misunderstood your use case.<br>
If you call <code>.cuda()</code> on an <code>nn.Parameter</code>, it won’t be a leaf variable anymore, which is explaiend <a href="https://discuss.pytorch.org/t/valueerror-cant-optimize-a-non-leaf-tensor/21751/2">here</a> and thus won’t appear in the <code>.parameters()</code>.</p>

copyrightly: <p>I see. Thank you very much for your explanation!</p>