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The tick stayed in the kitchen, sipping beer, spreading his weak moustache with a forefinger and thumb, looking well-pleased.

'He's going to help us with our enquiries into the murder of a young girl.'

'Murder?' she said, moving to embrace him as if he'd been condemned already.

'Let's go,' he said, turning away from her.

We got in the car. Valentim rested an elbow on the window ledge, and played drum solos on the roof with his fingers as we drove back into town in the highest heat of the day.

'Where's your father?' I asked.

'He pulled out years ago, I don't remember him.'

'How old were you.'

'Too small to remember.'

'You did all right to get to university.'

'Not if you look at the chatos in my class.'

'How do you like your mother?'

'She's my mother… that's it.'

'How old is she?'

'What do you think?'

'I don't know. It's difficult to say…'

'With all the make-up?'

'The guy she's with looks young.'

'She's thirty-seven. OK?'

'But do you like her?'

He stopped tapping on the roof.

'Where did they find you?' he asked. 'Winged on the motorway?'

'I'm one of the few people you'll meet in my world with an interest in other human beings… but that doesn't mean I'm sweet all the time. Now tell me what you think of your mother.'

'This is shit,' he said, enunciating each word with precision. 'You're the one reading psychology at university.' He sighed, bored to his hair roots.

'I think my mother's a beautiful person with a strong moral and ethical purpose, profoundly concerned with…'

'You've answered the question,' I said. 'Now… do you have a girlfriend at the moment?'

'No.'

'You've had girlfriends?'

'Occasionally. Temporarily.'

'What attracted you to these girls?'

'Do you write for Cosmopolitan in your spare time?'

'It's either this or the elbow in the face.'

'The girls always came to me. '

'All that highly-charged magnetism of yours.'

'I was stating a fact. I did not pursue them. They came to me.'

'What sort of girls?'

'Middle-class girls from well-off families who wanted to be different, who wanted to be cool, who wanted to have a go with someone who wasn't a trussed-up jerk with a mobile phone that never rang.'

'But you were too strong for them. Too rich. No. Wrong word. Too gamey.'

'They're not real people, Inspector. They're just kids dressing up.'

'And Catarina… was she like that?'

He nodded and smirked as if he'd seen my thread.

'You're forgetting something,' he said. 'Catarina was never my girlfriend.'

'But it was interesting wasn't it,' I said, 'because you found her.'

'Found her?'

'Discovered her voice. Brought her into the band. You pursued her. She didn't come to you.'

'That doesn't mean she was…'

'But it was different wasn't it?'

He drummed on the roof again.

I had a small fight to get into the PJ building with the policeman on the door who knew me well, but didn't believe who I was until I showed him some ID with my bearded self on it. Was this the start of a good old-fashioned identity crisis?

I left Valentim at the front desk and went upstairs to find Carlos and Bruno sitting in my office, both silent. I read the statement and told Bruno to sign it.

'Did Valentim have an arrangement to see Catarina after school on Friday?'

'She always went back to Cascais on Fridays.'

'Did you see Valentim on Friday night?'

'Yes. We met up in Alcantara around ten o'clock.'

'What was he doing between two and ten o'clock?'

'I don't know.'

'Was he agitated when you saw him?'

'No.'

'Teresa said Catarina had been promiscuous around the university. Is that true?'

'Not if Teresa said it. That would not be reliable.'

'She says she saw Catarina with her chemistry lecturer in the Bairro Alto later on Wednesday night after the band bust up.'

'I wouldn't know.'

'Where did you go after the band meeting?'

'Home. I worked late on a paper I had to deliver on Thursday morning.'

'And Valentim and Catarina?'

'I left them in that bar, Toca, in the Bairro Alto.'

We went to the stairs and I told him to wait five minutes before he went home. Carlos and I took Valentim to the Pensao Nuno which was on Rua da Gloria, a narrow road that ran between the Praca da Alegria and the funicular from Restauradores up to the Bairro Alto. There weren't many hookers around in the street at this time of day. A few older and sadder ones looked out of the bar windows sitting over coffee. Valentim's face in the rear view was straight out of the mould, solid.

The reception was on the second floor of a four-storey nineteenth-century building with a tiled facade up to the first-floor balcony. The staircase was wide, wooden and musty with a strip of blue lino up the middle. A guy in his sixties was standing behind the reception bar, a newspaper in front of him, his finger on his tongue. A strip of neon lighting on the wall above his grey head lit cobwebs and other high grime. He was unshaven and smoked a cigarette unconsciously. He looked as if he had been fat and then lost it and been left with useless folds of skin that sagged in his shirt.

He glanced up at us, and I saw it in his eyes that he knew he was looking at two policemen and a suspect.

He stood up straight and put a hand under his armpit. He ran a thumbnail through the brisdes below his bottom lip. The smoke made him close an eye. His skin looked grey as if ingrained by dust from some previous work such as mining.

'Are you Nuno?' I asked.

'He's dead.'

'Who are you?'

'Jorge.'

'You run this place?'

He smoked and nodded.

'I know who you are,' he said.

'So you don't need to see any ID.'

'You can still show it to me.'

We laid our cards out. He inspected them closely without touching.

'You look better without,' he said to me.

'You know this kid?' I asked.

Jorge's eyes went sleepy in his head as if he was a python who'd eaten a horse and was finding the hooves difficult to digest. He smoked some more, stubbed out the cigarette with a grimace and showed us a set of yellow teeth that hadn't met floss.

'You're going to tell me he's been here before and I'm going to have to believe you but…' he trailed off, took out his reservations book and flicked through empty pages.

'Maybe you should get the "rooms by the hour" edition out.'

'If they occupy…'

'We want to take a look at a room on the top floor. Are they all free?'

'If they're locked they're occupied.'

'Are you busy?' I asked, and Jorge made some calculations. 'I'm going into every room, locked or not.'

He hitched his trousers and slid out from behind the bar. He was wearing flip-flops and his yellow toenails, thick as tile, matched his teeth. I followed the dead skin on his crusty heels up to the top floor.

'How many rooms up here?'

'Four,' he said, economical now that the stairs were taking his puff.

At the top he coughed himself to a tremulous silence and spat into a handkerchief.

'Well?' he said, waving a finger at Valentim.

'Don't ask me,' said Valentim. 'I don't know what I'm doing here.'

'You remember what I said about the elbow in the face?' I asked.

'You heard that?' he said to Jorge. 'That was a threat.'

'I don't see you. I don't hear him,' said Jorge. 'All my senses got worn down years ago.'

Valentim looked at one of the doors and Jorge opened it up with a flourish from his hand like a nineteenth-century doorman.

Inside Valentim took up a position on the other side of the bed from me. Carlos sat on a sciatic chair by the door which he'd just closed. I washed my hands in the sink, looked at Valentim in the mirror and dabbed my face cool with wet palms. I shook my hands dry, straightened my tie and took my jacket off. It was hot in the room even with the shutters closed.