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At 08.30 I put a call in to Dr Aquilino Dias Oliveira who I assumed was the girl's father and, given his two addresses in Lisbon and Cascais, was not engaged in the great financial struggle that the rest of us were. It was a Saturday so I tried the Cascais number first and thought I was wrong until he picked it up at the twelfth ring and groggily agreed to see us in half an hour's time. We got into my black 1972 Alfa Romeo, which was not, as many thought, a classic car, just an old car, and it started without having to draw on any reserves of bravery. We headed west on the Marginal with Carlos pinned to his seat by the belt that was stuck at one length and for a girl Olivia's size.

There were big fans of Cascais but I wasn't one of them. It used to be a small fishing village with houses falling down steep cataracts of cobbled streets to the harbour and port. Now it was a townplanner's nightmare, unless you were one of the townplanners who'd passed the numerous development projects in which case you'd be living in a dream elsewhere. It was a tourist town with an indigenous population of women who dressed to shop, and men who shouldn't be allowed out of a nightclub. Real life had been stripped out and replaced with an international cosmopolitanism which appealed to a lot of people who had money, and about as many again who wanted to ease it away from them.

We rolled in past the supermarket, the railway station and an electronic signboard which told us that it was 28°C at 08.55 and we should get some insurance. The fish market was wrapping up for the morning. The lobster and crab pots were piled high in front of the Hotel Bahia. The fort, square and ugly, out on the point, dominated. I drove up a cobbled street at the back of the town hall and turned into a tree-lined, heavily shaded square, cool and sombre with wealth, in the old part of town. Dr Oliveira's traditional villa on two floors was large and silent in the breathless morning. Carlos Pinto sniffed like a dog that's picked up the whiff of the first possible scrap of the day.

'Pine,' he said.

'The pine needle angle could be a lot of work in this area, agente Pinto.'

'There's a pine tree in the back garden,' he said looking down the side of the house.

We let ourselves in by the front gate and went past a pillar of red bougainvillea to the back of the house. The pine tree was huge and shut out the light to the garden. The floor beneath it was a perfect brown carpet of dried needles.

'Put your foot on that,' I said.

Carlos' foot crunched through a couple of inches of needles.

'I don't think you could kill someone on that and leave it…'

'Bom dia, senhores,' said a voice behind us. 'And you are…?'

'We were admiring your pine tree,' said Carlos, electing to be the idiot.

'I'm going to cut it down,' said the thin, tall, erect man with white brilliantined hair, combed in rails off a high forehead and curling at the collar. 'It kills the light in the back of the house and makes the maid feel gloomy. You are the Policia Judiciaria, I take it?'

We introduced ourselves and followed him into the house. He wore a lightweight, English chequered shirt, grey slacks with turnups and brown loafers. He walked with his hands behind his back and stooped a little like a thoughtful priest. The parquet-floored corridor was lined with portraits of ancestors depressed at being cooped up in the dark. His study had more parquet flooring and Arraiolos carpets of some quality and antiquity. His desk was large and made out of walnut and had a brown leather chair behind it which was shiny where he'd buffed it with his back. Four lamps, supported by polished women carved from jet, provided light. The red bougainvillea outside had eclipsed the sunshine. He sat us down at a three-piece suite in a book-lined corner of the room. Only a lawyer would have so many books in the same bindings. An ormolu clock ticked as if each tick was going to be its last.

Dr Oliveira was in no hurry to talk. As we sat down he fitted his dark-skinned face into a pair of bifocals and searched his desk for something he didn't find. The maid came in and laid out coffee without looking at us. There was a photograph of the dead girl on a shelf squeezed in between some old paperbacks, thrillers, written in English.

Catarina Oliveira was smiling at the camera. Her blue eyes were wide open but they didn't match what her mouth was doing. Something tightened in my chest. I'd seen the same look in Olivia's eyes after I'd told her that her mother was dead.

That's her,' said Dr Oliveira, his white eyebrows jumping over the frames of his bifocals.

He was old for the father of a fifteen-year-old girl-late sixties in his body and more than that in the lines and creases of his face and neck. He should have been trying to remember the names of his grandchildren. He leaned forward and picked out a small cigar from a jade box on the desk top. He licked his lips which became the colour of pig's liver and screwed the cigar between them. He lit it. The maid rattled a coffee cup down in front of him and reversed out of the room.

'When did you last see her?' I asked, putting the photograph back.

'Thursday night. I left my Lisbon house early on Friday morning. I had to get to my office to prepare for a day in court.'

'What sort of law do you practise?'

'Corporate law. Tax. I've never done criminal work if you think that's relevant.'

'Did your wife see Catarina on Friday morning?'

'She dropped her off at school and came down here. It's what she does in the summer at the weekends.'

'And Catarina makes her own way here after school… on the train… from Cais do Sodre?'

'She's usually here by six or seven o'clock.'

'She was reported missing at nine.'

'I got back here at about half-past-eight. My wife had been here about an hour worrying, we phoned everybody we could think of and then I reported her missing at…'

'Does she have any particular friends? A boyfriend?'

'She sings in a band. She spends most of her spare time with them,' he said, leaning back with his coffee. 'Boyfriends? None that I know of.'

'Is that a school band?'

'They're all at the university. Two boys-Valentim and Bruno-and a girl. The girl is called… Teresa. Yes. Teresa, that's it.'

'All of them a lot older than Catarina.'

'They must be twenty, twenty-one, the boys. The girl, I don't know. Probably the same but she wears black and uses purple lipstick so it's difficult to tell.'

'We'll need all their details,' I said, and Dr Oliveira reached for a pad and began leafing through his address book. He scribbled down names and addresses. 'Is she your only child?'

'From this marriage, yes. I have four grown-up children. Teresa…' he let the name drift with his cigar smoke, his eyes glanced at a photograph on his desk.

'Is that your current wife?' I asked, and looked at the same photograph, which was of the four children from his previous marriage.

'My second wife,' he replied, annoyed with himself. 'Catarina's her only child.'

'Is your wife here, Senhor Doutor?' I asked.

'She's upstairs. She's not well. She's sleeping. She takes… she's taken something to help her sleep. I don't think it would be a good idea…'

'Is she a nervous woman… ordinarily?'

'When it comes to Catarina, when it comes to her only daughter missing the whole night, when it comes to a phone call from the Policia Judiciaria first thing in the morning… then yes, she becomes…'

'How would you describe their present relationship? Catarina and your wife.'

'What?' he said, looking across to Carlos as if he might be able to clarify this sort of question.

'It's not always a simple relationship-mother and daughter.'

'I don't know what you're driving at,' he said, coughing a half-laugh.

'The Chinese character for "strife" is represented by two women under the same roof.'

Dr Aquilino Oliveira supported himself with the heels of his palms on the edge of the desk and looked out at me over the rims of his glasses. His dark brown eyes reached in.

'She's never run off without a word before,' he said, quietly.