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'She walked straight in there and took her clothes off.'

'Do you think she was on drugs?'

'Maybe.' He ducked his head.

'Did she take money from you?'

'Yes, until I hid my wallet.'

'Did that annoy her?'

'She didn't comment.'

'How many times did she come here?'

'Ten, twelve times.'

'And why didn't she come back after the nineteenth of March?'

'She did. I just didn't let her in.'

He nodded back at the bedroom door and we looked over there too.

We left a little after that and sat in the car outside. The girlfriend came out a few minutes after us, taking strides far too long for her legs, her stacked heels wobbling on the calcada. Carlos nodded, satisfied that the girl had seen what he had.

'That guy,' he said, ' novo rico.'

We drove back to the lawyer's house. I had a couple of questions for Teresa but Dr Oliveira wouldn't allow it until she came into the corridor and beckoned us in. She was moving like an old woman and her speech was slow and drifting at the edges.

'The day you found Catarina in bed with Paulo Branco… why did you go back to the house?'

'I don't remember.'

'Weren't you already here?'

'I was.'

'It must have been something important to go all the way back into Lisbon.'

She didn't say anything. I apologized and stood to leave. Her face had sagged. Pouches that hadn't been there before appeared below her eyes.

'I went back,' she said, so tired she could hardly get it out, 'because Catarina called me. She said she'd hurt herself at school.'

The three of us exchanged looks. She held her hands open to show us how life could be.

'That was the end of me and Catarina,' she said.

We drove back to the 2° Circular around Lisbon in silence. I liked Carlos for this. No need to ask questions for which neither of us had any answers. He was contemplative. A different man to the edgy one he'd revealed on the beach and in Paulo Branco's flat. I doubted he had many friends.

I was feeling sick at how a family like the Oliveiras could go so wrong. The family. The strongest unit of Portuguese currency. Our gold. Our greatest asset. The pure element that keeps our streets mostly clean. Nobody in Europe understands the value of family better than us and it's not just leftover Salazarist propaganda. Was this where society's cracks started to appear?

We were heading for a massive development on the north edge of Lisbon called Odivelas. We skirted one of our present glories-Colombo, the biggest shopping centre in Europe-opposite one of the older ones-Benfica stadium, toying with bankruptcy. We curved off and back under the 2° Circular and headed uphill. At the top we had the best view there was of Odivelas-twenty square kilometres of distressed tower blocks, covered in a frazzled hair of clustered television aerials. It was a hellish vision, a construction company's Elysium. They built these things in weeks-concrete skeleton bones, skin walls with no fat-they were baking in the summer and freezing in the winter. I've never been able to breathe in them, the air's been re-used too much.

We walked up the stairs to the fourth floor of a block which was part of a development within another development. This block was one of the originals, the rest clones. The lift didn't work. Tiles were broken and missing underfoot, and the concrete walls had encrustations from dried damp. Televisions squabbled between floors. Music and the smell of lunches piped down the stairwell. A couple of kids bounced off the walls and squeezed past us.

We knocked on a cardboard door where we were hoping to find the lead guitarist from Catarina's band. The man who opened the door was thin, with what looked like a badly applied moustache of the same lank texture as the dark hair on his head. He wore a purple short-sleeved shirt open all the way down. His hand was on his chest where he stroked the hair around his nipples with the two fingers he used for smoking. He knew we were police.

'Is Valentim Mateus Almeida in?' I asked.

He turned without speaking. We followed him down the narrow corridor. He tapped on a door as he was passing.

'Valentim,' he said. 'Police.'

He carried on into the kitchen where an overweight woman with bleached hair, who'd squeezed herself into a turquoise skirt, was clearing away lunch. She asked him who'd been at the door. He told her, and she sucked in her stomach. We knocked on Valentim's door again. The place smelled of fried fish.

Valentim invited us in but didn't look up from where he was sitting on the bed playing an electric guitar, unplugged. He had a huge thick swag of long dark brown ringlets, sheafed down the length of his back. He wore a T-shirt and jeans. He was thin, olive-skinned with big dark eyes and hollow, underfed cheeks. Carlos closed the door of the narrow room which had a bed, a desk but no bookcase. The books were piled on the floor. Some of them were in English and French.

'Your father's not too concerned about the quality of your visitors.'

'That's because he's not my father, not even my stepfather. He's just the resident asshole who keeps my mother from getting lonely… and don't worry, I've told her.'

'What?' asked Carlos.

'That it's better to be lonely than live with a tick, but then… she'd scratch him off and get another one in its place. That's the nature of ticks and those they feed on.'

'Are you reading zoology?'

'Psychology,' he said. 'Zoology's something I live with. It creeps under my door.'

'You know a girl called Catarina Sousa Oliveira?'

'I know her,' he said, going back to his fingerwork on the guitar.

'She's dead. Murdered.'

His fingers stopped. He took the guitar by the neck and leaned it against a chair at the end of the bed. He was thinking, composing himself, but shocked too.

'I didn't know.'

'We're reconstructing her last twenty-four hours.'

'I haven't seen her,' he said, quickly.

'Not for twenty-four hours?'

'No.'

'Did you speak to her?'

'No.'

'When did you last see her?'

'Wednesday evening.'

'What happened?'

'The band met to talk about the weekend gig and rehearsals for Friday and Saturday.'

'Yesterday was Friday,' said Carlos.

'Thanks for reminding me. One day's like the next in Odivelas,' he said. 'The band also bust up on Wednesday. There was no rehearsal, there will be no gig.'

'Why did you bust up?'

'Musical differences,' he said. 'Teresa, she's the keyboard player… she's fucking some guy who plays the saxophone, so she thinks we suddenly need a saxophonist. She thinks we need to do more instrumental stuff. I said…'

'Less emphasis on the lead singer?' said Carlos.

Valentim turned to me for an opinion.

'I can't help you there,' I said. 'Nothing's happened in my life since Pink Floyd.'

'How musical were these differences?' asked Carlos.

'That's your first decent question and you go and answer it yourself.'

'What about Bruno, what does he play?'

'Bass.'

'Were either you or Bruno going out with Catarina?' I asked.

'Going out?'

'Were you fucking her?' said Carlos, picking up words as we went along.

'We had a "no relationships" agreement in the band.'

'The saxophonist didn't have a chance.'

'I don't suppose he did.'

'The meeting. Where did it take place?'

'In a bar called Toca. It's in the Bairro Alto.'

'And you didn't see her after that-not on Thursday, nor Friday?'

'No.'

'Do you know what she was doing yesterday?'

'She went to school, didn't she?'

'Where were you?'

'In the Biblioteca Nacional… all day… until seven, seven-thirty.'

I gave him a card and told him to call me if he remembered anything. Valentim's mother was looking down the corridor from the kitchen when we came out. I gave her a good afternoon which brought the tick to her shoulder.

'Where was Valentim yesterday?' I asked.

'He was out all day and most of the night,' said the tick. 'Didn't get in until three in the morning.'